LMFDB - Embedded newform 98.8.c.d.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,8,Mod(67,98)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.6137324974$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.8.c.d.67.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-6.00000 - 10.3923i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(105.000 - 181.865i) q^{5} -96.0000 q^{6} -512.000 q^{8} +(1021.50 - 1769.29i) q^{9} +(-840.000 - 1454.92i) q^{10} +(-546.000 - 945.700i) q^{11} +(-384.000 + 665.108i) q^{12} +1382.00 q^{13} -2520.00 q^{15} +(-2048.00 + 3547.24i) q^{16} +(-7353.00 - 12735.8i) q^{17} +(-8172.00 - 14154.3i) q^{18} +(19970.0 - 34589.1i) q^{19} -13440.0 q^{20} -8736.00 q^{22} +(-34356.0 + 59506.3i) q^{23} +(3072.00 + 5320.86i) q^{24} +(17012.5 + 29466.5i) q^{25} +(5528.00 - 9574.78i) q^{26} -50760.0 q^{27} -102570. q^{29} +(-10080.0 + 17459.1i) q^{30} +(-113776. - 197066. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-6552.00 + 11348.4i) q^{33} -117648. q^{34} -130752. q^{36} +(-80263.0 + 139020. i) q^{37} +(-159760. - 276712. i) q^{38} +(-8292.00 - 14362.2i) q^{39} +(-53760.0 + 93115.1i) q^{40} +10842.0 q^{41} -630748. q^{43} +(-34944.0 + 60524.8i) q^{44} +(-214515. - 371551. i) q^{45} +(274848. + 476051. i) q^{46} +(-236328. + 409332. i) q^{47} +49152.0 q^{48} +272200. q^{50} +(-88236.0 + 152829. i) q^{51} +(-44224.0 - 76598.2i) q^{52} +(747009. + 1.29386e6i) q^{53} +(-203040. + 351676. i) q^{54} -229320. q^{55} -479280. q^{57} +(-410280. + 710626. i) q^{58} +(-1.32033e6 - 2.28688e6i) q^{59} +(80640.0 + 139673. i) q^{60} +(-413851. + 716811. i) q^{61} -1.82042e6 q^{62} +262144. q^{64} +(145110. - 251338. i) q^{65} +(52416.0 + 90787.2i) q^{66} +(63002.0 + 109123. i) q^{67} +(-470592. + 815089. i) q^{68} +824544. q^{69} -1.41473e6 q^{71} +(-523008. + 905876. i) q^{72} +(-490141. - 848949. i) q^{73} +(642104. + 1.11216e6i) q^{74} +(204150. - 353598. i) q^{75} -2.55616e6 q^{76} -132672. q^{78} +(1.78340e6 - 3.08894e6i) q^{79} +(430080. + 744920. i) q^{80} +(-1.92946e6 - 3.34192e6i) q^{81} +(43368.0 - 75115.6i) q^{82} +5.67289e6 q^{83} -3.08826e6 q^{85} +(-2.52299e6 + 4.36995e6i) q^{86} +(615420. + 1.06594e6i) q^{87} +(279552. + 484198. i) q^{88} +(5.97560e6 - 1.03500e7i) q^{89} -3.43224e6 q^{90} +4.39757e6 q^{92} +(-1.36531e6 + 2.36479e6i) q^{93} +(1.89062e6 + 3.27466e6i) q^{94} +(-4.19370e6 - 7.26370e6i) q^{95} +(196608. - 340535. i) q^{96} +8.68215e6 q^{97} -2.23096e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 12 q^{3} - 64 q^{4} + 210 q^{5} - 192 q^{6} - 1024 q^{8} + 2043 q^{9} - 1680 q^{10} - 1092 q^{11} - 768 q^{12} + 2764 q^{13} - 5040 q^{15} - 4096 q^{16} - 14706 q^{17} - 16344 q^{18} + 39940 q^{19}+ \cdots - 4461912 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 - 12 * q^3 - 64 * q^4 + 210 * q^5 - 192 * q^6 - 1024 * q^8 + 2043 * q^9 - 1680 * q^10 - 1092 * q^11 - 768 * q^12 + 2764 * q^13 - 5040 * q^15 - 4096 * q^16 - 14706 * q^17 - 16344 * q^18 + 39940 * q^19 - 26880 * q^20 - 17472 * q^22 - 68712 * q^23 + 6144 * q^24 + 34025 * q^25 + 11056 * q^26 - 101520 * q^27 - 205140 * q^29 - 20160 * q^30 - 227552 * q^31 + 32768 * q^32 - 13104 * q^33 - 235296 * q^34 - 261504 * q^36 - 160526 * q^37 - 319520 * q^38 - 16584 * q^39 - 107520 * q^40 + 21684 * q^41 - 1261496 * q^43 - 69888 * q^44 - 429030 * q^45 + 549696 * q^46 - 472656 * q^47 + 98304 * q^48 + 544400 * q^50 - 176472 * q^51 - 88448 * q^52 + 1494018 * q^53 - 406080 * q^54 - 458640 * q^55 - 958560 * q^57 - 820560 * q^58 - 2640660 * q^59 + 161280 * q^60 - 827702 * q^61 - 3640832 * q^62 + 524288 * q^64 + 290220 * q^65 + 104832 * q^66 + 126004 * q^67 - 941184 * q^68 + 1649088 * q^69 - 2829456 * q^71 - 1046016 * q^72 - 980282 * q^73 + 1284208 * q^74 + 408300 * q^75 - 5112320 * q^76 - 265344 * q^78 + 3566800 * q^79 + 860160 * q^80 - 3858921 * q^81 + 86736 * q^82 + 11345784 * q^83 - 6176520 * q^85 - 5045984 * q^86 + 1230840 * q^87 + 559104 * q^88 + 11951190 * q^89 - 6864480 * q^90 + 8795136 * q^92 - 2730624 * q^93 + 3781248 * q^94 - 8387400 * q^95 + 393216 * q^96 + 17364292 * q^97 - 4461912 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$	−6.00000	−	10.3923i	−0.128300	−	0.222222i	0.794718	−	0.606979i	$-0.207619\pi$
$3$	−6.00000	−	10.3923i	−0.128300	−	0.222222i	−0.923018	+	0.384757i	$0.874285\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	105.000	−	181.865i	0.375659	−	0.650661i	−0.614766	−	0.788709i	$-0.710750\pi$
$5$	105.000	−	181.865i	0.375659	−	0.650661i	0.990425	+	0.138048i	$0.0440829\pi$
$6$	−96.0000			−0.181444
$7$		0			0
$7$		0			0
$8$	−512.000			−0.353553
$9$	1021.50	−	1769.29i	0.467078	−	0.809003i
$10$	−840.000	−	1454.92i	−0.265631	−	0.460087i
$11$	−546.000	−	945.700i	−0.123685	−	0.214229i	0.797533	−	0.603275i	$-0.206138\pi$
$11$	−546.000	−	945.700i	−0.123685	−	0.214229i	−0.921218	+	0.389046i	$0.872805\pi$
$12$	−384.000	+	665.108i	−0.0641500	+	0.111111i
$13$	1382.00			0.174464			0.0872321	−	0.996188i	$-0.472198\pi$
$13$	1382.00			0.174464			0.0872321	+	0.996188i	$0.472198\pi$
$14$		0			0
$15$	−2520.00			−0.192789
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−7353.00	−	12735.8i	−0.362989	−	0.628715i	0.625462	−	0.780254i	$-0.284910\pi$
$17$	−7353.00	−	12735.8i	−0.362989	−	0.628715i	−0.988451	+	0.151539i	$0.951577\pi$
$18$	−8172.00	−	14154.3i	−0.330274	−	0.572052i
$19$	19970.0	−	34589.1i	0.667945	−	1.15691i	−0.310533	−	0.950563i	$-0.600508\pi$
$19$	19970.0	−	34589.1i	0.667945	−	1.15691i	0.978478	−	0.206352i	$-0.0661590\pi$
$20$	−13440.0			−0.375659
$21$		0			0
$22$	−8736.00			−0.174917
$23$	−34356.0	+	59506.3i	−0.588783	+	1.01980i	0.405609	+	0.914047i	$0.367059\pi$
$23$	−34356.0	+	59506.3i	−0.588783	+	1.01980i	−0.994392	+	0.105755i	$0.966274\pi$
$24$	3072.00	+	5320.86i	0.0453609	+	0.0785674i
$25$	17012.5	+	29466.5i	0.217760	+	0.377171i
$26$	5528.00	−	9574.78i	0.0616824	−	0.106837i
$27$	−50760.0			−0.496305
$28$		0			0
$29$	−102570.			−0.780957			−0.390479	−	0.920612i	$-0.627690\pi$
$29$	−102570.			−0.780957			−0.390479	+	0.920612i	$0.627690\pi$
$30$	−10080.0	+	17459.1i	−0.0681610	+	0.118058i
$31$	−113776.	−	197066.i	−0.685938	−	1.18808i	−0.973141	−	0.230209i	$-0.926059\pi$
$31$	−113776.	−	197066.i	−0.685938	−	1.18808i	0.287203	−	0.957870i	$-0.407274\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$	−6552.00	+	11348.4i	−0.0317377	+	0.0549713i
$34$	−117648.			−0.513344
$35$		0			0
$36$	−130752.			−0.467078
$37$	−80263.0	+	139020.i	−0.260501	+	0.451201i	−0.966375	−	0.257136i	$-0.917221\pi$
$37$	−80263.0	+	139020.i	−0.260501	+	0.451201i	0.705874	+	0.708337i	$0.250554\pi$
$38$	−159760.	−	276712.i	−0.472308	−	0.818062i
$39$	−8292.00	−	14362.2i	−0.0223838	−	0.0387698i
$40$	−53760.0	+	93115.1i	−0.132816	+	0.230043i
$41$	10842.0			0.0245678			0.0122839	−	0.999925i	$-0.496090\pi$
$41$	10842.0			0.0245678			0.0122839	+	0.999925i	$0.496090\pi$
$42$		0			0
$43$	−630748.			−1.20981			−0.604904	−	0.796299i	$-0.706788\pi$
$43$	−630748.			−1.20981			−0.604904	+	0.796299i	$0.706788\pi$
$44$	−34944.0	+	60524.8i	−0.0618427	+	0.107115i
$45$	−214515.	−	371551.i	−0.350925	−	0.607819i
$46$	274848.	+	476051.i	0.416332	+	0.721109i
$47$	−236328.	+	409332.i	−0.332026	+	0.575087i	−0.982909	−	0.184092i	$-0.941066\pi$
$47$	−236328.	+	409332.i	−0.332026	+	0.575087i	0.650883	+	0.759178i	$0.274399\pi$
$48$	49152.0			0.0641500
$49$		0			0
$50$	272200.			0.307959
$51$	−88236.0	+	152829.i	−0.0931430	+	0.161328i
$52$	−44224.0	−	76598.2i	−0.0436160	−	0.0755452i
$53$	747009.	+	1.29386e6i	0.689224	+	1.19377i	0.972089	+	0.234611i	$0.0753817\pi$
$53$	747009.	+	1.29386e6i	0.689224	+	1.19377i	−0.282865	+	0.959160i	$0.591285\pi$
$54$	−203040.	+	351676.i	−0.175470	+	0.303923i
$55$	−229320.			−0.185854
$56$		0			0
$57$	−479280.			−0.342789
$58$	−410280.	+	710626.i	−0.276110	+	0.478237i
$59$	−1.32033e6	−	2.28688e6i	−0.836952	−	1.44964i	−0.892431	−	0.451183i	$-0.851002\pi$
$59$	−1.32033e6	−	2.28688e6i	−0.836952	−	1.44964i	0.0554795	−	0.998460i	$-0.482331\pi$
$60$	80640.0	+	139673.i	0.0481971	+	0.0834799i
$61$	−413851.	+	716811.i	−0.233448	+	0.404343i	−0.958820	−	0.284013i	$-0.908334\pi$
$61$	−413851.	+	716811.i	−0.233448	+	0.404343i	0.725373	+	0.688356i	$0.241667\pi$
$62$	−1.82042e6			−0.970063
$63$		0			0
$64$	262144.			0.125000
$65$	145110.	−	251338.i	0.0655391	−	0.113517i
$66$	52416.0	+	90787.2i	0.0224419	+	0.0388706i
$67$	63002.0	+	109123.i	0.0255913	+	0.0443255i	0.878537	−	0.477674i	$-0.158520\pi$
$67$	63002.0	+	109123.i	0.0255913	+	0.0443255i	−0.852946	+	0.521999i	$0.825186\pi$
$68$	−470592.	+	815089.i	−0.181494	+	0.314358i
$69$	824544.			0.302164
$70$		0			0
$71$	−1.41473e6			−0.469104			−0.234552	−	0.972104i	$-0.575362\pi$
$71$	−1.41473e6			−0.469104			−0.234552	+	0.972104i	$0.575362\pi$
$72$	−523008.	+	905876.i	−0.165137	+	0.286026i
$73$	−490141.	−	848949.i	−0.147466	−	0.255418i	0.782824	−	0.622243i	$-0.213778\pi$
$73$	−490141.	−	848949.i	−0.147466	−	0.255418i	−0.930290	+	0.366825i	$0.880445\pi$
$74$	642104.	+	1.11216e6i	0.184202	+	0.319047i
$75$	204150.	−	353598.i	0.0558772	−	0.0967822i
$76$	−2.55616e6			−0.667945
$77$		0			0
$78$	−132672.			−0.0316554
$79$	1.78340e6	−	3.08894e6i	0.406962	−	0.704879i	−0.587586	−	0.809162i	$-0.699921\pi$
$79$	1.78340e6	−	3.08894e6i	0.406962	−	0.704879i	0.994548	+	0.104283i	$0.0332548\pi$
$80$	430080.	+	744920.i	0.0939149	+	0.162665i
$81$	−1.92946e6	−	3.34192e6i	−0.403402	−	0.698713i
$82$	43368.0	−	75115.6i	0.00868602	−	0.0150446i
$83$	5.67289e6			1.08901			0.544504	−	0.838758i	$-0.316718\pi$
$83$	5.67289e6			1.08901			0.544504	+	0.838758i	$0.316718\pi$
$84$		0			0
$85$	−3.08826e6			−0.545441
$86$	−2.52299e6	+	4.36995e6i	−0.427732	+	0.740853i
$87$	615420.	+	1.06594e6i	0.100197	+	0.173546i
$88$	279552.	+	484198.i	0.0437294	+	0.0757415i
$89$	5.97560e6	−	1.03500e7i	0.898496	−	1.55624i	0.0690786	−	0.997611i	$-0.477994\pi$
$89$	5.97560e6	−	1.03500e7i	0.898496	−	1.55624i	0.829417	−	0.558629i	$-0.188673\pi$
$90$	−3.43224e6			−0.496282
$91$		0			0
$92$	4.39757e6			0.588783
$93$	−1.36531e6	+	2.36479e6i	−0.176012	+	0.304861i
$94$	1.89062e6	+	3.27466e6i	0.234778	+	0.406648i
$95$	−4.19370e6	−	7.26370e6i	−0.501839	−	0.869211i
$96$	196608.	−	340535.i	0.0226805	−	0.0392837i
$97$	8.68215e6			0.965886			0.482943	−	0.875652i	$-0.339568\pi$
$97$	8.68215e6			0.965886			0.482943	+	0.875652i	$0.339568\pi$
$98$		0			0
$99$	−2.23096e6			−0.231083
$100$	1.08880e6	−	1.88586e6i	0.108880	−	0.188586i
$101$	5.03977e6	+	8.72914e6i	0.486727	+	0.843037i	0.999884	−	0.0152586i	$-0.00485716\pi$
$101$	5.03977e6	+	8.72914e6i	0.486727	+	0.843037i	−0.513156	+	0.858295i	$0.671524\pi$
$102$	705888.	+	1.22263e6i	0.0658620	+	0.114076i
$103$	−1.87400e6	+	3.24586e6i	−0.168981	+	0.292684i	−0.938062	−	0.346468i	$-0.887381\pi$
$103$	−1.87400e6	+	3.24586e6i	−0.168981	+	0.292684i	0.769081	+	0.639152i	$0.220714\pi$
$104$	−707584.			−0.0616824
$105$		0			0
$106$	1.19521e7			0.974710
$107$	8.99278e6	−	1.55760e7i	0.709661	−	1.22917i	−0.255322	−	0.966856i	$-0.582182\pi$
$107$	8.99278e6	−	1.55760e7i	0.709661	−	1.22917i	0.964983	−	0.262313i	$-0.0844852\pi$
$108$	1.62432e6	+	2.81340e6i	0.124076	+	0.214906i
$109$	−6.12851e6	−	1.06149e7i	−0.453276	−	0.785097i	0.545311	−	0.838234i	$-0.316411\pi$
$109$	−6.12851e6	−	1.06149e7i	−0.453276	−	0.785097i	−0.998587	+	0.0531368i	$0.983078\pi$
$110$	−917280.	+	1.58878e6i	−0.0657094	+	0.113812i
$111$	1.92631e6			0.133689
$112$		0			0
$113$	1.65950e7			1.08194			0.540968	−	0.841043i	$-0.318058\pi$
$113$	1.65950e7			1.08194			0.540968	+	0.841043i	$0.318058\pi$
$114$	−1.91712e6	+	3.32055e6i	−0.121194	+	0.209915i
$115$	7.21476e6	+	1.24963e7i	0.442364	+	0.766196i
$116$	3.28224e6	+	5.68501e6i	0.195239	+	0.338164i
$117$	1.41171e6	−	2.44516e6i	0.0814884	−	0.141142i
$118$	−2.11253e7			−1.18363
$119$		0			0
$120$	1.29024e6			0.0681610
$121$	9.14735e6	−	1.58437e7i	0.469404	−	0.813031i
$122$	3.31081e6	+	5.73449e6i	0.165072	+	0.285914i
$123$	−65052.0	−	112673.i	−0.00315205	−	0.00545951i
$124$	−7.28166e6	+	1.26122e7i	−0.342969	+	0.594040i
$125$	2.35515e7			1.07853
$126$		0			0
$127$	1.16826e6			0.0506087			0.0253043	−	0.999680i	$-0.491945\pi$
$127$	1.16826e6			0.0506087			0.0253043	+	0.999680i	$0.491945\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$	3.78449e6	+	6.55493e6i	0.155218	+	0.268846i
$130$	−1.16088e6	−	2.01070e6i	−0.0463432	−	0.0802687i
$131$	3.96191e6	−	6.86224e6i	0.153977	−	0.266696i	−0.778709	−	0.627385i	$-0.784125\pi$
$131$	3.96191e6	−	6.86224e6i	0.153977	−	0.266696i	0.932686	+	0.360689i	$0.117459\pi$
$132$	838656.			0.0317377
$133$		0			0
$134$	1.00803e6			0.0361916
$135$	−5.32980e6	+	9.23148e6i	−0.186442	+	0.322926i
$136$	3.76474e6	+	6.52071e6i	0.128336	+	0.222284i
$137$	157827.	+	273364.i	0.00524396	+	0.00908280i	0.868635	−	0.495452i	$-0.164997\pi$
$137$	157827.	+	273364.i	0.00524396	+	0.00908280i	−0.863392	+	0.504535i	$0.831664\pi$
$138$	3.29818e6	−	5.71261e6i	0.106831	−	0.185037i
$139$	3.92038e7			1.23816			0.619079	−	0.785329i	$-0.287506\pi$
$139$	3.92038e7			1.23816			0.619079	+	0.785329i	$0.287506\pi$
$140$		0			0
$141$	5.67187e6			0.170396
$142$	−5.65891e6	+	9.80152e6i	−0.165853	+	0.287266i
$143$	−754572.	−	1.30696e6i	−0.0215787	−	0.0373753i
$144$	4.18406e6	+	7.24701e6i	0.116770	+	0.202251i
$145$	−1.07698e7	+	1.86539e7i	−0.293374	+	0.508139i
$146$	−7.84226e6			−0.208548
$147$		0			0
$148$	1.02737e7			0.260501
$149$	1.09430e7	−	1.89539e7i	0.271010	−	0.469403i	−0.698111	−	0.715990i	$-0.745976\pi$
$149$	1.09430e7	−	1.89539e7i	0.271010	−	0.469403i	0.969121	+	0.246587i	$0.0793090\pi$
$150$	−1.63320e6	−	2.82879e6i	−0.0395112	−	0.0684354i
$151$	1.47077e7	+	2.54745e7i	0.347637	+	0.602125i	0.985829	−	0.167752i	$-0.0536508\pi$
$151$	1.47077e7	+	2.54745e7i	0.347637	+	0.602125i	−0.638192	+	0.769877i	$0.720317\pi$
$152$	−1.02246e7	+	1.77096e7i	−0.236154	+	0.409031i
$153$	−3.00444e7			−0.678177
$154$		0			0
$155$	−4.77859e7			−1.03072
$156$	−530688.	+	919179.i	−0.0111919	+	0.0193849i
$157$	−3.02775e7	−	5.24421e7i	−0.624412	−	1.08151i	−0.988654	−	0.150209i	$-0.952005\pi$
$157$	−3.02775e7	−	5.24421e7i	−0.624412	−	1.08151i	0.364243	−	0.931304i	$-0.381328\pi$
$158$	−1.42672e7	−	2.47115e7i	−0.287766	−	0.498425i
$159$	8.96411e6	−	1.55263e7i	0.176855	−	0.306322i
$160$	6.88128e6			0.132816
$161$		0			0
$162$	−3.08714e7			−0.570497
$163$	−2.85426e7	+	4.94373e7i	−0.516223	+	0.894125i	0.483599	+	0.875290i	$0.339329\pi$
$163$	−2.85426e7	+	4.94373e7i	−0.516223	+	0.894125i	−0.999823	+	0.0188355i	$0.994004\pi$
$164$	−346944.	−	600925.i	−0.00614194	−	0.0106382i
$165$	1.37592e6	+	2.38316e6i	0.0238451	+	0.0413009i
$166$	2.26916e7	−	3.93029e7i	0.385023	−	0.666879i
$167$	−8.77265e7			−1.45755			−0.728775	−	0.684754i	$-0.759910\pi$
$167$	−8.77265e7			−1.45755			−0.728775	+	0.684754i	$0.759910\pi$
$168$		0			0
$169$	−6.08386e7			−0.969562
$170$	−1.23530e7	+	2.13961e7i	−0.192842	+	0.334013i
$171$	−4.07987e7	−	7.06654e7i	−0.623965	−	1.08074i
$172$	2.01839e7	+	3.49596e7i	0.302452	+	0.523862i
$173$	−4.28477e6	+	7.42144e6i	−0.0629167	+	0.108975i	−0.895768	−	0.444522i	$-0.853374\pi$
$173$	−4.28477e6	+	7.42144e6i	−0.0629167	+	0.108975i	0.832851	+	0.553497i	$0.186707\pi$
$174$	9.84672e6			0.141700
$175$		0			0
$176$	4.47283e6			0.0618427
$177$	−1.58440e7	+	2.74425e7i	−0.214762	+	0.371979i
$178$	−4.78048e7	−	8.28003e7i	−0.635333	−	1.10043i
$179$	−9.40203e6	−	1.62848e7i	−0.122528	−	0.212225i	0.798236	−	0.602345i	$-0.205767\pi$
$179$	−9.40203e6	−	1.62848e7i	−0.122528	−	0.212225i	−0.920764	+	0.390120i	$0.872434\pi$
$180$	−1.37290e7	+	2.37793e7i	−0.175462	+	0.303910i
$181$	−5.99625e7			−0.751631			−0.375816	−	0.926694i	$-0.622637\pi$
$181$	−5.99625e7			−0.751631			−0.375816	+	0.926694i	$0.622637\pi$
$182$		0			0
$183$	9.93242e6			0.119805
$184$	1.75903e7	−	3.04672e7i	0.208166	−	0.360554i
$185$	1.68552e7	+	2.91941e7i	0.195719	+	0.338996i
$186$	1.09225e7	+	1.89183e7i	0.124459	+	0.215569i
$187$	−8.02948e6	+	1.39075e7i	−0.0897928	+	0.155526i
$188$	3.02500e7			0.332026
$189$		0			0
$190$	−6.70992e7			−0.709708
$191$	−4.69931e7	+	8.13944e7i	−0.487997	+	0.845235i	−0.999905	−	0.0138052i	$-0.995606\pi$
$191$	−4.69931e7	+	8.13944e7i	−0.487997	+	0.845235i	0.511908	+	0.859040i	$0.328939\pi$
$192$	−1.57286e6	−	2.72428e6i	−0.0160375	−	0.0277778i
$193$	1.75973e7	+	3.04794e7i	0.176196	+	0.305180i	0.940574	−	0.339588i	$-0.110288\pi$
$193$	1.75973e7	+	3.04794e7i	0.176196	+	0.305180i	−0.764379	+	0.644767i	$0.776954\pi$
$194$	3.47286e7	−	6.01517e7i	0.341492	−	0.591482i
$195$	−3.48264e6			−0.0336347
$196$		0			0
$197$	1.02985e8			0.959718			0.479859	−	0.877346i	$-0.340688\pi$
$197$	1.02985e8			0.959718			0.479859	+	0.877346i	$0.340688\pi$
$198$	−8.92382e6	+	1.54565e7i	−0.0817001	+	0.141509i
$199$	−4.18188e7	−	7.24323e7i	−0.376171	−	0.651548i	0.614330	−	0.789049i	$-0.289426\pi$
$199$	−4.18188e7	−	7.24323e7i	−0.376171	−	0.651548i	−0.990502	+	0.137501i	$0.956093\pi$
$200$	−8.71040e6	−	1.50869e7i	−0.0769898	−	0.133350i
$201$	756024.	−	1.30947e6i	0.00656673	−	0.0113739i
$202$	8.06363e7			0.688337
$203$		0			0
$204$	1.12942e7			0.0931430
$205$	1.13841e6	−	1.97178e6i	0.00922912	−	0.0159853i
$206$	1.49920e7	+	2.59669e7i	0.119488	+	0.206959i
$207$	7.01893e7	+	1.21571e8i	0.550015	+	0.952654i
$208$	−2.83034e6	+	4.90229e6i	−0.0218080	+	0.0377726i
$209$	−4.36145e7			−0.330460
$210$		0			0
$211$	−9.74010e7			−0.713797			−0.356899	−	0.934143i	$-0.616166\pi$
$211$	−9.74010e7			−0.713797			−0.356899	+	0.934143i	$0.616166\pi$
$212$	4.78086e7	−	8.28069e7i	0.344612	−	0.596885i
$213$	8.48837e6	+	1.47023e7i	0.0601860	+	0.104245i
$214$	−7.19423e7	−	1.24608e8i	−0.501806	−	0.869153i
$215$	−6.62285e7	+	1.14711e8i	−0.454476	+	0.787175i
$216$	2.59891e7			0.175470
$217$		0			0
$218$	−9.80562e7			−0.641029
$219$	−5.88169e6	+	1.01874e7i	−0.0378397	+	0.0655403i
$220$	7.33824e6	+	1.27102e7i	0.0464636	+	0.0804773i
$221$	−1.01618e7	−	1.76008e7i	−0.0633286	−	0.109688i
$222$	7.70525e6	−	1.33459e7i	0.0472663	−	0.0818676i
$223$	−1.46457e7			−0.0884390			−0.0442195	−	0.999022i	$-0.514080\pi$
$223$	−1.46457e7			−0.0884390			−0.0442195	+	0.999022i	$0.514080\pi$
$224$		0			0
$225$	6.95131e7			0.406844
$226$	6.63798e7	−	1.14973e8i	0.382522	−	0.662548i
$227$	9.22704e7	+	1.59817e8i	0.523567	+	0.906844i	0.999624	+	0.0274298i	$0.00873228\pi$
$227$	9.22704e7	+	1.59817e8i	0.523567	+	0.906844i	−0.476057	+	0.879414i	$0.657934\pi$
$228$	1.53370e7	+	2.65644e7i	0.0856973	+	0.148432i
$229$	4.37730e6	−	7.58171e6i	0.0240870	−	0.0417199i	−0.853731	−	0.520715i	$-0.825665\pi$
$229$	4.37730e6	−	7.58171e6i	0.0240870	−	0.0417199i	0.877818	+	0.478995i	$0.158999\pi$
$230$	1.15436e8			0.625597
$231$		0			0
$232$	5.25158e7			0.276110
$233$	5.97781e7	−	1.03539e8i	0.309597	−	0.536237i	−0.668677	−	0.743553i	$-0.733139\pi$
$233$	5.97781e7	−	1.03539e8i	0.309597	−	0.536237i	0.978274	+	0.207315i	$0.0664726\pi$
$234$	−1.12937e7	−	1.95613e7i	−0.0576210	−	0.0998025i
$235$	4.96289e7	+	8.59597e7i	0.249458	+	0.432073i
$236$	−8.45011e7	+	1.46360e8i	−0.418476	+	0.724822i
$237$	−4.28016e7			−0.208853
$238$		0			0
$239$	3.96209e8			1.87729			0.938646	−	0.344883i	$-0.112081\pi$
$239$	3.96209e8			1.87729			0.938646	+	0.344883i	$0.112081\pi$
$240$	5.16096e6	−	8.93904e6i	0.0240986	−	0.0417399i
$241$	1.28303e8	+	2.22228e8i	0.590443	+	1.02268i	0.994173	+	0.107799i	$0.0343801\pi$
$241$	1.28303e8	+	2.22228e8i	0.590443	+	1.02268i	−0.403730	+	0.914878i	$0.632287\pi$
$242$	−7.31788e7	−	1.26749e8i	−0.331919	−	0.574900i
$243$	−7.86596e7	+	1.36242e8i	−0.351665	+	0.609102i
$244$	5.29729e7			0.233448
$245$		0			0
$246$	−1.04083e6			−0.00445767
$247$	2.75985e7	−	4.78021e7i	0.116532	−	0.201840i
$248$	5.82533e7	+	1.00898e8i	0.242516	+	0.420049i
$249$	−3.40374e7	−	5.89544e7i	−0.139720	−	0.242002i
$250$	9.42060e7	−	1.63170e8i	0.381319	−	0.660464i
$251$	−7.34775e7			−0.293290			−0.146645	−	0.989189i	$-0.546847\pi$
$251$	−7.34775e7			−0.293290			−0.146645	+	0.989189i	$0.546847\pi$
$252$		0			0
$253$	7.50335e7			0.291295
$254$	4.67302e6	−	8.09391e6i	0.0178929	−	0.0309914i
$255$	1.85296e7	+	3.20941e7i	0.0699801	+	0.121209i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	1.01351e8	−	1.75544e8i	0.372443	−	0.645091i	−0.617498	−	0.786573i	$-0.711853\pi$
$257$	1.01351e8	−	1.75544e8i	0.372443	−	0.645091i	0.989941	+	0.141482i	$0.0451868\pi$
$258$	6.05518e7			0.219512
$259$		0			0
$260$	−1.85741e7			−0.0655391
$261$	−1.04775e8	+	1.81476e8i	−0.364768	+	0.631797i
$262$	−3.16953e7	−	5.48979e7i	−0.108878	−	0.188582i
$263$	−7.71270e7	−	1.33588e8i	−0.261434	−	0.452816i	0.705189	−	0.709019i	$-0.250862\pi$
$263$	−7.71270e7	−	1.33588e8i	−0.261434	−	0.452816i	−0.966623	+	0.256203i	$0.917529\pi$
$264$	3.35462e6	−	5.81038e6i	0.0112210	−	0.0194353i
$265$	3.13744e8			1.03565
$266$		0			0
$267$	−1.43414e8			−0.461108
$268$	4.03213e6	−	6.98385e6i	0.0127957	−	0.0221627i
$269$	3.12009e8	+	5.40416e8i	0.977315	+	1.69276i	0.672075	+	0.740483i	$0.265403\pi$
$269$	3.12009e8	+	5.40416e8i	0.977315	+	1.69276i	0.305239	+	0.952276i	$0.401264\pi$
$270$	4.26384e7	+	7.38519e7i	0.131834	+	0.228343i
$271$	1.93992e8	−	3.36003e8i	0.592094	−	1.02554i	−0.401856	−	0.915703i	$-0.631635\pi$
$271$	1.93992e8	−	3.36003e8i	0.592094	−	1.02554i	0.993950	−	0.109834i	$-0.0350318\pi$
$272$	6.02358e7			0.181494
$273$		0			0
$274$	2.52523e6			0.00741608
$275$	1.85776e7	−	3.21774e7i	0.0538674	−	0.0933011i
$276$	−2.63854e7	−	4.57009e7i	−0.0755409	−	0.130841i
$277$	−2.26976e8	−	3.93134e8i	−0.641654	−	1.11138i	−0.985063	−	0.172192i	$-0.944915\pi$
$277$	−2.26976e8	−	3.93134e8i	−0.641654	−	1.11138i	0.343409	−	0.939186i	$-0.388418\pi$
$278$	1.56815e8	−	2.71612e8i	0.437755	−	0.758214i
$279$	−4.64889e8			−1.28155
$280$		0			0
$281$	3.33770e8			0.897377			0.448689	−	0.893688i	$-0.351891\pi$
$281$	3.33770e8			0.897377			0.448689	+	0.893688i	$0.351891\pi$
$282$	2.26875e7	−	3.92959e7i	0.0602441	−	0.104346i
$283$	−2.68847e8	−	4.65657e8i	−0.705104	−	1.22128i	−0.966654	−	0.256086i	$-0.917567\pi$
$283$	−2.68847e8	−	4.65657e8i	−0.705104	−	1.22128i	0.261550	−	0.965190i	$-0.415766\pi$
$284$	4.52713e7	+	7.84122e7i	0.117276	+	0.203128i
$285$	−5.03244e7	+	8.71644e7i	−0.128772	+	0.223040i
$286$	−1.20732e7			−0.0305168
$287$		0			0
$288$	6.69450e7			0.165137
$289$	9.70361e7	−	1.68071e8i	0.236478	−	0.409592i
$290$	8.61588e7	+	1.49231e8i	0.207447	+	0.359308i
$291$	−5.20929e7	−	9.02275e7i	−0.123923	−	0.214641i
$292$	−3.13690e7	+	5.43327e7i	−0.0737329	+	0.127709i
$293$	3.35600e8			0.779445			0.389722	−	0.920932i	$-0.372571\pi$
$293$	3.35600e8			0.779445			0.389722	+	0.920932i	$0.372571\pi$
$294$		0			0
$295$	−5.54539e8			−1.25764
$296$	4.10947e7	−	7.11780e7i	0.0921010	−	0.159524i
$297$	2.77150e7	+	4.80037e7i	0.0613856	+	0.106323i
$298$	−8.75442e7	−	1.51631e8i	−0.191633	−	0.331918i
$299$	−4.74800e7	+	8.22378e7i	−0.102722	+	0.177919i
$300$	−2.61312e7			−0.0558772
$301$		0			0
$302$	2.35324e8			0.491633
$303$	6.04772e7	−	1.04750e8i	0.124894	−	0.216323i
$304$	8.17971e7	+	1.41677e8i	0.166986	+	0.289229i
$305$	8.69087e7	+	1.50530e8i	0.175394	+	0.303791i
$306$	−1.20177e8	+	2.08153e8i	−0.239772	+	0.415297i
$307$	2.15029e8			0.424143			0.212072	−	0.977254i	$-0.431979\pi$
$307$	2.15029e8			0.424143			0.212072	+	0.977254i	$0.431979\pi$
$308$		0			0
$309$	4.49759e7			0.0867212
$310$	−1.91144e8	+	3.31071e8i	−0.364413	+	0.631182i
$311$	−3.96031e8	−	6.85945e8i	−0.746565	−	1.29309i	−0.949460	−	0.313888i	$-0.898368\pi$
$311$	−3.96031e8	−	6.85945e8i	−0.746565	−	1.29309i	0.202895	−	0.979200i	$-0.434965\pi$
$312$	4.24550e6	+	7.35343e6i	0.00791386	+	0.0137072i
$313$	5.92287e7	−	1.02587e8i	0.109176	−	0.189098i	−0.806261	−	0.591560i	$-0.798512\pi$
$313$	5.92287e7	−	1.02587e8i	0.109176	−	0.189098i	0.915437	+	0.402462i	$0.131845\pi$
$314$	−4.84440e8			−0.883051
$315$		0			0
$316$	−2.28275e8			−0.406962
$317$	2.53655e7	−	4.39343e7i	0.0447235	−	0.0774633i	−0.842797	−	0.538231i	$-0.819093\pi$
$317$	2.53655e7	−	4.39343e7i	0.0447235	−	0.0774633i	0.887521	+	0.460768i	$0.152426\pi$
$318$	−7.17129e7	−	1.24210e8i	−0.125055	−	0.216602i
$319$	5.60032e7	+	9.70004e7i	0.0965930	+	0.167304i
$320$	2.75251e7	−	4.76749e7i	0.0469574	−	0.0813327i
$321$	−2.15827e8			−0.364198
$322$		0			0
$323$	−5.87358e8			−0.969826
$324$	−1.23485e8	+	2.13883e8i	−0.201701	+	0.349357i
$325$	2.35113e7	+	4.07227e7i	0.0379913	+	0.0658029i
$326$	2.28341e8	+	3.95499e8i	0.365025	+	0.632242i
$327$	−7.35422e7	+	1.27379e8i	−0.116311	+	0.201456i
$328$	−5.55110e6			−0.00868602
$329$		0			0
$330$	2.20147e7			0.0337221
$331$	−1.36878e8	+	2.37080e8i	−0.207461	+	0.359334i	−0.950914	−	0.309455i	$-0.899853\pi$
$331$	−1.36878e8	+	2.37080e8i	−0.207461	+	0.359334i	0.743453	+	0.668788i	$0.233187\pi$
$332$	−1.81533e8	−	3.14424e8i	−0.272252	−	0.471554i
$333$	1.63977e8	+	2.84017e8i	0.243349	+	0.421492i
$334$	−3.50906e8	+	6.07787e8i	−0.515321	+	0.892563i
$335$	2.64608e7			0.0384545
$336$		0			0
$337$	−9.18512e7			−0.130732			−0.0653658	−	0.997861i	$-0.520821\pi$
$337$	−9.18512e7			−0.130732			−0.0653658	+	0.997861i	$0.520821\pi$
$338$	−2.43354e8	+	4.21502e8i	−0.342792	+	0.593733i
$339$	−9.95698e7	−	1.72460e8i	−0.138812	−	0.240430i
$340$	9.88243e7	+	1.71169e8i	0.136360	+	0.236183i
$341$	−1.24243e8	+	2.15196e8i	−0.169681	+	0.293896i
$342$	−6.52779e8			−0.882419
$343$		0			0
$344$	3.22943e8			0.427732
$345$	8.65771e7	−	1.49956e8i	0.113511	−	0.196606i
$346$	3.42782e7	+	5.93715e7i	0.0444889	+	0.0770570i
$347$	6.83502e8	+	1.18386e9i	0.878187	+	1.52106i	0.853329	+	0.521373i	$0.174580\pi$
$347$	6.83502e8	+	1.18386e9i	0.878187	+	1.52106i	0.0248578	+	0.999691i	$0.492087\pi$
$348$	3.93869e7	−	6.82201e7i	0.0500984	−	0.0867730i
$349$	1.13143e9			1.42475			0.712377	−	0.701797i	$-0.247619\pi$
$349$	1.13143e9			1.42475			0.712377	+	0.701797i	$0.247619\pi$
$350$		0			0
$351$	−7.01503e7			−0.0865874
$352$	1.78913e7	−	3.09887e7i	0.0218647	−	0.0378707i
$353$	2.24198e7	+	3.88322e7i	0.0271281	+	0.0469873i	0.879271	−	0.476322i	$-0.158030\pi$
$353$	2.24198e7	+	3.88322e7i	0.0271281	+	0.0469873i	−0.852143	+	0.523310i	$0.824697\pi$
$354$	1.26752e8	+	2.19540e8i	0.151860	+	0.263029i
$355$	−1.48546e8	+	2.57290e8i	−0.176223	+	0.305227i
$356$	−7.64876e8			−0.898496
$357$		0			0
$358$	−1.50432e8			−0.173281
$359$	−1.99140e8	+	3.44921e8i	−0.227158	+	0.393450i	−0.956965	−	0.290204i	$-0.906277\pi$
$359$	−1.99140e8	+	3.44921e8i	−0.227158	+	0.393450i	0.729806	+	0.683654i	$0.239610\pi$
$360$	1.09832e8	+	1.90234e8i	0.124071	+	0.214897i
$361$	−3.50666e8	−	6.07371e8i	−0.392300	−	0.679484i
$362$	−2.39850e8	+	4.15432e8i	−0.265742	+	0.460278i
$363$	−2.19536e8			−0.240898
$364$		0			0
$365$	−2.05859e8			−0.221588
$366$	3.97297e7	−	6.88139e7i	0.0423576	−	0.0733655i
$367$	−8.17359e8	−	1.41571e9i	−0.863140	−	1.49500i	−0.868882	−	0.495020i	$-0.835161\pi$
$367$	−8.17359e8	−	1.41571e9i	−0.863140	−	1.49500i	0.00574132	−	0.999984i	$-0.498172\pi$
$368$	−1.40722e8	−	2.43738e8i	−0.147196	−	0.254950i
$369$	1.10751e7	−	1.91826e7i	0.0114751	−	0.0198754i
$370$	2.69684e8			0.276789
$371$		0			0
$372$	1.74760e8			0.176012
$373$	7.73166e8	−	1.33916e9i	0.771421	−	1.33614i	−0.165363	−	0.986233i	$-0.552879\pi$
$373$	7.73166e8	−	1.33916e9i	0.771421	−	1.33614i	0.936784	−	0.349908i	$-0.113787\pi$
$374$	6.42358e7	+	1.11260e8i	0.0634931	+	0.109973i
$375$	−1.41309e8	−	2.44754e8i	−0.138376	−	0.239674i
$376$	1.21000e8	−	2.09578e8i	0.117389	−	0.203324i
$377$	−1.41752e8			−0.136249
$378$		0			0
$379$	−1.05688e9			−0.997216			−0.498608	−	0.866828i	$-0.666155\pi$
$379$	−1.05688e9			−0.997216			−0.498608	+	0.866828i	$0.666155\pi$
$380$	−2.68397e8	+	4.64877e8i	−0.250920	+	0.434606i
$381$	−7.00954e6	−	1.21409e7i	−0.00649310	−	0.0112464i
$382$	3.75944e8	+	6.51155e8i	0.345066	+	0.597671i
$383$	−1.12455e8	+	1.94778e8i	−0.102278	+	0.177151i	−0.912623	−	0.408802i	$-0.865947\pi$
$383$	−1.12455e8	+	1.94778e8i	−0.102278	+	0.177151i	0.810345	+	0.585953i	$0.199280\pi$
$384$	−2.51658e7			−0.0226805
$385$		0			0
$386$	2.81556e8			0.249178
$387$	−6.44309e8	+	1.11598e9i	−0.565075	+	0.978738i
$388$	−2.77829e8	−	4.81213e8i	−0.241472	−	0.418241i
$389$	−5.08941e8	−	8.81512e8i	−0.438373	−	0.759284i	0.559191	−	0.829039i	$-0.311112\pi$
$389$	−5.08941e8	−	8.81512e8i	−0.438373	−	0.759284i	−0.997564	+	0.0697544i	$0.977778\pi$
$390$	−1.39306e7	+	2.41284e7i	−0.0118917	+	0.0205970i
$391$	1.01048e9			0.854887
$392$		0			0
$393$	−9.50859e7			−0.0790210
$394$	4.11941e8	−	7.13503e8i	0.339311	−	0.587705i
$395$	−3.74514e8	−	6.48677e8i	−0.305758	−	0.529589i
$396$	7.13906e7	+	1.23652e8i	0.0577707	+	0.100062i
$397$	7.37826e8	−	1.27795e9i	0.591817	−	1.02506i	−0.402171	−	0.915565i	$-0.631744\pi$
$397$	7.37826e8	−	1.27795e9i	0.591817	−	1.02506i	0.993988	−	0.109492i	$-0.0349225\pi$
$398$	−6.69100e8			−0.531986
$399$		0			0
$400$	−1.39366e8			−0.108880
$401$	−1.37456e8	+	2.38081e8i	−0.106453	+	0.184382i	−0.914331	−	0.404968i	$-0.867283\pi$
$401$	−1.37456e8	+	2.38081e8i	−0.106453	+	0.184382i	0.807878	+	0.589350i	$0.200616\pi$
$402$	−6.04819e6	−	1.04758e7i	−0.00464338	−	0.00804257i
$403$	−1.57238e8	−	2.72345e8i	−0.119672	−	0.207277i
$404$	3.22545e8	−	5.58665e8i	0.243364	−	0.421518i
$405$	−8.10373e8			−0.606167
$406$		0			0
$407$	1.75294e8			0.128881
$408$	4.51768e7	−	7.82486e7i	0.0329310	−	0.0570382i
$409$	8.17136e8	+	1.41532e9i	0.590558	+	1.02288i	0.994157	+	0.107941i	$0.0344258\pi$
$409$	8.17136e8	+	1.41532e9i	0.590558	+	1.02288i	−0.403599	+	0.914936i	$0.632241\pi$
$410$	−9.10728e6	−	1.57743e7i	−0.00652597	−	0.0113033i
$411$	1.89392e6	−	3.28037e6i	0.00134560	−	0.00233065i
$412$	2.39871e8			0.168981
$413$		0			0
$414$	1.12303e9			0.777839
$415$	5.95654e8	−	1.03170e9i	0.409096	−	0.708575i
$416$	2.26427e7	+	3.92183e7i	0.0154206	+	0.0267093i
$417$	−2.35223e8	−	4.07418e8i	−0.158856	−	0.275146i
$418$	−1.74458e8	+	3.02170e8i	−0.116835	+	0.202365i
$419$	−1.11280e9			−0.739039			−0.369519	−	0.929223i	$-0.620478\pi$
$419$	−1.11280e9			−0.739039			−0.369519	+	0.929223i	$0.620478\pi$
$420$		0			0
$421$	9.22528e8			0.602549			0.301274	−	0.953537i	$-0.402588\pi$
$421$	9.22528e8			0.602549			0.301274	+	0.953537i	$0.402588\pi$
$422$	−3.89604e8	+	6.74814e8i	−0.252365	+	0.437110i
$423$	4.82818e8	+	8.36265e8i	0.310165	+	0.537221i
$424$	−3.82469e8	−	6.62455e8i	−0.243677	−	0.422062i
$425$	2.50186e8	−	4.33335e8i	0.158089	−	0.273818i
$426$	1.35814e8			0.0851159
$427$		0			0
$428$	−1.15108e9			−0.709661
$429$	−9.05486e6	+	1.56835e7i	−0.00553709	+	0.00959052i
$430$	5.29828e8	+	9.17690e8i	0.321363	+	0.556617i
$431$	4.90754e8	+	8.50011e8i	0.295252	+	0.511392i	0.975044	−	0.222014i	$-0.0712629\pi$
$431$	4.90754e8	+	8.50011e8i	0.295252	+	0.511392i	−0.679791	+	0.733406i	$0.737930\pi$
$432$	1.03956e8	−	1.80058e8i	0.0620381	−	0.107453i
$433$	2.84998e9			1.68707			0.843537	−	0.537071i	$-0.180469\pi$
$433$	2.84998e9			1.68707			0.843537	+	0.537071i	$0.180469\pi$
$434$		0			0
$435$	2.58476e8			0.150560
$436$	−3.92225e8	+	6.79354e8i	−0.226638	+	0.392548i
$437$	1.37218e9	+	2.37668e9i	0.786549	+	1.36234i
$438$	4.70535e7	+	8.14991e7i	0.0267567	+	0.0463440i
$439$	5.28109e8	−	9.14712e8i	0.297919	−	0.516011i	−0.677741	−	0.735301i	$-0.737041\pi$
$439$	5.28109e8	−	9.14712e8i	0.297919	−	0.516011i	0.975660	+	0.219290i	$0.0703742\pi$
$440$	1.17412e8			0.0657094
$441$		0			0
$442$	−1.62590e8			−0.0895601
$443$	−9.11627e8	+	1.57899e9i	−0.498201	+	0.862909i	−0.999998	−	0.00207637i	$-0.999339\pi$
$443$	−9.11627e8	+	1.57899e9i	−0.498201	+	0.862909i	0.501797	+	0.864985i	$0.332672\pi$
$444$	−6.16420e7	−	1.06767e8i	−0.0334223	−	0.0578891i
$445$	−1.25487e9	−	2.17351e9i	−0.675057	−	1.16923i
$446$	−5.85829e7	+	1.01469e8i	−0.0312679	+	0.0541576i
$447$	−2.62633e8			−0.139082
$448$		0			0
$449$	1.84846e9			0.963713			0.481856	−	0.876250i	$-0.339963\pi$
$449$	1.84846e9			0.963713			0.481856	+	0.876250i	$0.339963\pi$
$450$	2.78052e8	−	4.81601e8i	0.143841	−	0.249140i
$451$	−5.91973e6	−	1.02533e7i	−0.00303867	−	0.00526314i
$452$	−5.31039e8	−	9.19786e8i	−0.270484	−	0.468492i
$453$	1.76493e8	−	3.05694e8i	0.0892037	−	0.154505i
$454$	1.47633e9			0.740435
$455$		0			0
$456$	2.45391e8			0.121194
$457$	1.49033e9	−	2.58133e9i	0.730425	−	1.26513i	−0.226276	−	0.974063i	$-0.572655\pi$
$457$	1.49033e9	−	2.58133e9i	0.730425	−	1.26513i	0.956702	−	0.291071i	$-0.0940114\pi$
$458$	−3.50184e7	−	6.06537e7i	−0.0170321	−	0.0295004i
$459$	3.73238e8	+	6.46468e8i	0.180153	+	0.312034i
$460$	4.61745e8	−	7.99765e8i	0.221182	−	0.383098i
$461$	−2.52781e9			−1.20169			−0.600843	−	0.799367i	$-0.705168\pi$
$461$	−2.52781e9			−1.20169			−0.600843	+	0.799367i	$0.705168\pi$
$462$		0			0
$463$	−8.90291e8			−0.416868			−0.208434	−	0.978036i	$-0.566837\pi$
$463$	−8.90291e8			−0.416868			−0.208434	+	0.978036i	$0.566837\pi$
$464$	2.10063e8	−	3.63840e8i	0.0976197	−	0.169082i
$465$	2.86716e8	+	4.96606e8i	0.132241	+	0.229048i
$466$	−4.78225e8	−	8.28310e8i	−0.218918	−	0.379177i
$467$	−1.32833e9	+	2.30074e9i	−0.603529	+	1.04534i	0.388753	+	0.921342i	$0.372906\pi$
$467$	−1.32833e9	+	2.30074e9i	−0.603529	+	1.04534i	−0.992282	+	0.124001i	$0.960427\pi$
$468$	−1.80699e8			−0.0814884
$469$		0			0
$470$	7.94062e8			0.352786
$471$	−3.63330e8	+	6.29306e8i	−0.160224	+	0.277516i
$472$	6.76009e8	+	1.17088e9i	0.295907	+	0.512526i
$473$	3.44388e8	+	5.96498e8i	0.149635	+	0.259176i
$474$	−1.71206e8	+	2.96538e8i	−0.0738407	+	0.127896i
$475$	1.35896e9			0.581806
$476$		0			0
$477$	3.05228e9			1.28769
$478$	1.58484e9	−	2.74502e9i	0.663723	−	1.14960i
$479$	−6.50467e8	−	1.12664e9i	−0.270428	−	0.468394i	0.698544	−	0.715567i	$-0.253832\pi$
$479$	−6.50467e8	−	1.12664e9i	−0.270428	−	0.468394i	−0.968971	+	0.247173i	$0.920498\pi$
$480$	−4.12877e7	−	7.15124e7i	−0.0170403	−	0.0295146i
$481$	−1.10923e8	+	1.92125e8i	−0.0454481	+	0.0787184i
$482$	2.05285e9			0.835012
$483$		0			0
$484$	−1.17086e9			−0.469404
$485$	9.11625e8	−	1.57898e9i	0.362844	−	0.628465i
$486$	6.29277e8	+	1.08994e9i	0.248665	+	0.430700i
$487$	5.37233e8	+	9.30515e8i	0.210771	+	0.365066i	0.951956	−	0.306234i	$-0.0990692\pi$
$487$	5.37233e8	+	9.30515e8i	0.210771	+	0.365066i	−0.741185	+	0.671301i	$0.765736\pi$
$488$	2.11892e8	−	3.67007e8i	0.0825362	−	0.142957i
$489$	6.85024e8			0.264926
$490$		0			0
$491$	−7.83344e8			−0.298653			−0.149327	−	0.988788i	$-0.547711\pi$
$491$	−7.83344e8			−0.298653			−0.149327	+	0.988788i	$0.547711\pi$
$492$	−4.16333e6	+	7.21110e6i	−0.00157602	+	0.00272975i
$493$	7.54197e8	+	1.30631e9i	0.283479	+	0.491000i
$494$	−2.20788e8	−	3.82417e8i	−0.0824009	−	0.142722i
$495$	−2.34250e8	+	4.05734e8i	−0.0868085	+	0.150357i
$496$	9.32053e8			0.342969
$497$		0			0
$498$	−5.44598e8			−0.197594
$499$	3.11594e8	−	5.39697e8i	0.112263	−	0.194445i	−0.804419	−	0.594062i	$-0.797523\pi$
$499$	3.11594e8	−	5.39697e8i	0.112263	−	0.194445i	0.916682	+	0.399617i	$0.130857\pi$
$500$	−7.53648e8	−	1.30536e9i	−0.269633	−	0.467019i
$501$	5.26359e8	+	9.11681e8i	0.187004	+	0.323900i
$502$	−2.93910e8	+	5.09067e8i	−0.103694	+	0.179602i
$503$	−2.70927e9			−0.949215			−0.474607	−	0.880198i	$-0.657410\pi$
$503$	−2.70927e9			−0.949215			−0.474607	+	0.880198i	$0.657410\pi$
$504$		0			0
$505$	2.11670e9			0.731375
$506$	3.00134e8	−	5.19847e8i	0.102988	−	0.178381i
$507$	3.65032e8	+	6.32253e8i	0.124395	+	0.215458i
$508$	−3.73842e7	−	6.47513e7i	−0.0126522	−	0.0219142i
$509$	−1.74972e9	+	3.03060e9i	−0.588106	+	1.01863i	0.406374	+	0.913707i	$0.366793\pi$
$509$	−1.74972e9	+	3.03060e9i	−0.588106	+	1.01863i	−0.994480	+	0.104923i	$0.966540\pi$
$510$	2.96473e8			0.0989668
$511$		0			0
$512$	−1.34218e8			−0.0441942
$513$	−1.01368e9	+	1.75574e9i	−0.331504	+	0.574182i
$514$	−8.10804e8	−	1.40435e9i	−0.263357	−	0.456148i
$515$	3.93539e8	+	6.81630e8i	0.126959	+	0.219899i
$516$	2.42207e8	−	4.19515e8i	0.0776092	−	0.134423i
$517$	5.16140e8			0.164267
$518$		0			0
$519$	1.02835e8			0.0322889
$520$	−7.42963e7	+	1.28685e8i	−0.0231716	+	0.0401343i
$521$	6.88417e8	+	1.19237e9i	0.213265	+	0.369386i	0.952734	−	0.303804i	$-0.0982569\pi$
$521$	6.88417e8	+	1.19237e9i	0.213265	+	0.369386i	−0.739470	+	0.673190i	$0.764924\pi$
$522$	8.38202e8	+	1.45181e9i	0.257930	+	0.446748i
$523$	1.43077e9	−	2.47817e9i	0.437334	−	0.757486i	−0.560148	−	0.828392i	$-0.689256\pi$
$523$	1.43077e9	−	2.47817e9i	0.437334	−	0.757486i	0.997483	+	0.0709067i	$0.0225893\pi$
$524$	−5.07125e8			−0.153977
$525$		0			0
$526$	−1.23403e9			−0.369723
$527$	−1.67319e9	+	2.89805e9i	−0.497976	+	0.862519i
$528$	−2.68370e7	−	4.64830e7i	−0.00793442	−	0.0137428i
$529$	−6.58257e8	−	1.14013e9i	−0.193331	−	0.334858i
$530$	1.25498e9	−	2.17368e9i	0.366159	−	0.634206i
$531$	−5.39487e9			−1.56369
$532$		0			0
$533$	1.49836e7			0.00428620
$534$	−5.73657e8	+	9.93603e8i	−0.163026	+	0.282370i
$535$	−1.88848e9	−	3.27095e9i	−0.533182	−	0.923498i
$536$	−3.22570e7	−	5.58708e7i	−0.00904789	−	0.0156714i
$537$	−1.12824e8	+	1.95418e8i	−0.0314407	+	0.0544570i
$538$	4.99215e9			1.38213
$539$		0			0
$540$	6.82214e8			0.186442
$541$	−2.67234e9	+	4.62862e9i	−0.725605	+	1.25679i	0.233119	+	0.972448i	$0.425107\pi$
$541$	−2.67234e9	+	4.62862e9i	−0.725605	+	1.25679i	−0.958724	+	0.284337i	$0.908226\pi$
$542$	−1.55193e9	−	2.68803e9i	−0.418673	−	0.725164i
$543$	3.59775e8	+	6.23149e8i	0.0964343	+	0.167029i
$544$	2.40943e8	−	4.17326e8i	0.0641680	−	0.111142i
$545$	−2.57398e9			−0.681109
$546$		0			0
$547$	−3.37135e9			−0.880740			−0.440370	−	0.897816i	$-0.645153\pi$
$547$	−3.37135e9			−0.880740			−0.440370	+	0.897816i	$0.645153\pi$
$548$	1.01009e7	−	1.74953e7i	0.00262198	−	0.00454140i
$549$	8.45498e8	+	1.46444e9i	0.218077	+	0.377720i
$550$	−1.48621e8	−	2.57419e8i	−0.0380900	−	0.0659739i
$551$	−2.04832e9	+	3.54780e9i	−0.521636	+	0.903501i
$552$	−4.22167e8			−0.106831
$553$		0			0
$554$	−3.63162e9			−0.907436
$555$	2.02263e8	−	3.50329e8i	0.0502216	−	0.0869864i
$556$	−1.25452e9	−	2.17289e9i	−0.309540	−	0.536138i
$557$	2.80553e9	+	4.85932e9i	0.687894	+	1.19147i	0.972518	+	0.232828i	$0.0747980\pi$
$557$	2.80553e9	+	4.85932e9i	0.687894	+	1.19147i	−0.284624	+	0.958639i	$0.591869\pi$
$558$	−1.85955e9	+	3.22084e9i	−0.453095	+	0.784784i
$559$	−8.71694e8			−0.211068
$560$		0			0
$561$	1.92707e8			0.0460817
$562$	1.33508e9	−	2.31243e9i	0.317271	−	0.549529i
$563$	−3.34845e9	−	5.79968e9i	−0.790795	−	1.36970i	−0.925475	−	0.378809i	$-0.876334\pi$
$563$	−3.34845e9	−	5.79968e9i	−0.790795	−	1.36970i	0.134680	−	0.990889i	$-0.456999\pi$
$564$	−1.81500e8	−	3.14367e8i	−0.0425990	−	0.0737837i
$565$	1.74247e9	−	3.01805e9i	0.406440	−	0.703974i
$566$	−4.30156e9			−0.997168
$567$		0			0
$568$	7.24341e8			0.165853
$569$	−9.84251e8	+	1.70477e9i	−0.223982	+	0.387948i	−0.956013	−	0.293323i	$-0.905239\pi$
$569$	−9.84251e8	+	1.70477e9i	−0.223982	+	0.387948i	0.732032	+	0.681271i	$0.238572\pi$
$570$	4.02595e8	+	6.97315e8i	0.0910556	+	0.157713i
$571$	−5.14629e8	−	8.91363e8i	−0.115682	−	0.200368i	0.802370	−	0.596827i	$-0.203572\pi$
$571$	−5.14629e8	−	8.91363e8i	−0.115682	−	0.200368i	−0.918052	+	0.396459i	$0.870239\pi$
$572$	−4.82926e7	+	8.36453e7i	−0.0107893	+	0.0186877i
$573$	1.12783e9			0.250440
$574$		0			0
$575$	−2.33793e9			−0.512853
$576$	2.67780e8	−	4.63809e8i	0.0583848	−	0.101125i
$577$	−1.65590e9	−	2.86810e9i	−0.358854	−	0.621553i	0.628916	−	0.777473i	$-0.283499\pi$
$577$	−1.65590e9	−	2.86810e9i	−0.358854	−	0.621553i	−0.987770	+	0.155920i	$0.950166\pi$
$578$	−7.76289e8	−	1.34457e9i	−0.167215	−	0.289625i
$579$	2.11167e8	−	3.65753e8i	0.0452118	−	0.0783091i
$580$	1.37854e9			0.293374
$581$		0			0
$582$	−8.33486e8			−0.175254
$583$	8.15734e8	−	1.41289e9i	0.170494	−	0.295304i
$584$	2.50952e8	+	4.34662e8i	0.0521370	+	0.0903039i
$585$	−2.96460e8	−	5.13483e8i	−0.0612238	−	0.106043i
$586$	1.34240e9	−	2.32511e9i	0.275575	−	0.477311i
$587$	−5.59411e8			−0.114156			−0.0570778	−	0.998370i	$-0.518178\pi$
$587$	−5.59411e8			−0.114156			−0.0570778	+	0.998370i	$0.518178\pi$
$588$		0			0
$589$	−9.08843e9			−1.83267
$590$	−2.21815e9	+	3.84196e9i	−0.444641	+	0.770141i
$591$	−6.17912e8	−	1.07025e9i	−0.123132	−	0.213271i
$592$	−3.28757e8	−	5.69424e8i	−0.0651252	−	0.112800i
$593$	1.51229e9	−	2.61937e9i	0.297814	−	0.515829i	−0.677822	−	0.735226i	$-0.737076\pi$
$593$	1.51229e9	−	2.61937e9i	0.297814	−	0.515829i	0.975636	+	0.219398i	$0.0704092\pi$
$594$	4.43439e8			0.0868124
$595$		0			0
$596$	−1.40071e9			−0.271010
$597$	−5.01825e8	+	8.69187e8i	−0.0965256	+	0.167187i
$598$	3.79840e8	+	6.57902e8i	0.0726351	+	0.125808i
$599$	2.81623e9	+	4.87785e9i	0.535395	+	0.927331i	0.999144	+	0.0413648i	$0.0131706\pi$
$599$	2.81623e9	+	4.87785e9i	0.535395	+	0.927331i	−0.463749	+	0.885967i	$0.653496\pi$
$600$	−1.04525e8	+	1.81042e8i	−0.0197556	+	0.0342177i
$601$	3.40792e8			0.0640366			0.0320183	−	0.999487i	$-0.489807\pi$
$601$	3.40792e8			0.0640366			0.0320183	+	0.999487i	$0.489807\pi$
$602$		0			0
$603$	2.57426e8			0.0478126
$604$	9.41294e8	−	1.63037e9i	0.173819	−	0.301063i
$605$	−1.92094e9	−	3.32717e9i	−0.352672	−	0.610846i
$606$	−4.83818e8	−	8.37997e8i	−0.0883136	−	0.152964i
$607$	−1.92710e9	+	3.33783e9i	−0.349739	+	0.605765i	−0.986203	−	0.165541i	$-0.947063\pi$
$607$	−1.92710e9	+	3.33783e9i	−0.349739	+	0.605765i	0.636464	+	0.771306i	$0.280396\pi$
$608$	1.30875e9			0.236154
$609$		0			0
$610$	1.39054e9			0.248044
$611$	−3.26605e8	+	5.65697e8i	−0.0579267	+	0.100332i
$612$	9.61419e8	+	1.66523e9i	0.169544	+	0.293659i
$613$	−4.61122e9	−	7.98687e9i	−0.808545	−	1.40044i	−0.913871	−	0.406004i	$-0.866922\pi$
$613$	−4.61122e9	−	7.98687e9i	−0.808545	−	1.40044i	0.105326	−	0.994438i	$-0.466411\pi$
$614$	8.60116e8	−	1.48976e9i	0.149957	−	0.259734i
$615$	−2.73218e7			−0.00473639
$616$		0			0
$617$	6.53611e9			1.12027			0.560133	−	0.828402i	$-0.310750\pi$
$617$	6.53611e9			1.12027			0.560133	+	0.828402i	$0.310750\pi$
$618$	1.79904e8	−	3.11602e8i	0.0306606	−	0.0531057i
$619$	−6.82793e8	−	1.18263e9i	−0.115710	−	0.200416i	0.802353	−	0.596849i	$-0.203581\pi$
$619$	−6.82793e8	−	1.18263e9i	−0.115710	−	0.200416i	−0.918063	+	0.396434i	$0.870248\pi$
$620$	1.52915e9	+	2.64856e9i	0.257679	+	0.446313i
$621$	1.74391e9	−	3.02054e9i	0.292216	−	0.506133i
$622$	−6.33649e9			−1.05580
$623$		0			0
$624$	6.79281e7			0.0111919
$625$	1.14381e9	−	1.98113e9i	0.187401	−	0.324588i
$626$	−4.73830e8	−	8.20697e8i	−0.0771991	−	0.133713i
$627$	2.61687e8	+	4.53255e8i	0.0423980	+	0.0734355i
$628$	−1.93776e9	+	3.35630e9i	−0.312206	+	0.540756i
$629$	2.36070e9			0.378236
$630$		0			0
$631$	1.54079e9			0.244141			0.122070	−	0.992521i	$-0.461047\pi$
$631$	1.54079e9			0.244141			0.122070	+	0.992521i	$0.461047\pi$
$632$	−9.13101e8	+	1.58154e9i	−0.143883	+	0.249212i
$633$	5.84406e8	+	1.01222e9i	0.0915802	+	0.158622i
$634$	−2.02924e8	−	3.51474e8i	−0.0316243	−	0.0547749i
$635$	1.22667e8	−	2.12465e8i	0.0190116	−	0.0329291i
$636$	−1.14741e9			−0.176855
$637$		0			0
$638$	8.96052e8			0.136603
$639$	−1.44514e9	+	2.50306e9i	−0.219108	+	0.379506i
$640$	−2.20201e8	−	3.81399e8i	−0.0332039	−	0.0575109i
$641$	2.27009e9	+	3.93191e9i	0.340440	+	0.589659i	0.984514	−	0.175304i	$-0.0560908\pi$
$641$	2.27009e9	+	3.93191e9i	0.340440	+	0.589659i	−0.644075	+	0.764963i	$0.722757\pi$
$642$	−8.63307e8	+	1.49529e9i	−0.128763	+	0.223025i
$643$	1.14054e10			1.69189			0.845944	−	0.533272i	$-0.179038\pi$
$643$	1.14054e10			1.69189			0.845944	+	0.533272i	$0.179038\pi$
$644$		0			0
$645$	1.58948e9			0.233237
$646$	−2.34943e9	+	4.06933e9i	−0.342885	+	0.593895i
$647$	6.31967e9	+	1.09460e10i	0.917338	+	1.58888i	0.803442	+	0.595383i	$0.203000\pi$
$647$	6.31967e9	+	1.09460e10i	0.917338	+	1.58888i	0.113896	+	0.993493i	$0.463667\pi$
$648$	9.87884e8	+	1.71106e9i	0.142624	+	0.247032i
$649$	−1.44180e9	+	2.49727e9i	−0.207037	+	0.358599i
$650$	3.76180e8			0.0537278
$651$		0			0
$652$	3.65346e9			0.516223
$653$	5.25022e9	−	9.09365e9i	0.737873	−	1.27803i	−0.215579	−	0.976486i	$-0.569164\pi$
$653$	5.25022e9	−	9.09365e9i	0.737873	−	1.27803i	0.953451	−	0.301547i	$-0.0975029\pi$
$654$	5.88337e8	+	1.01903e9i	0.0822440	+	0.142451i
$655$	−8.32002e8	−	1.44107e9i	−0.115686	−	0.200374i
$656$	−2.22044e7	+	3.84592e7i	−0.00307097	+	0.00531908i
$657$	−2.00272e9			−0.275512
$658$		0			0
$659$	9.64818e9			1.31325			0.656624	−	0.754219i	$-0.271984\pi$
$659$	9.64818e9			1.31325			0.656624	+	0.754219i	$0.271984\pi$
$660$	8.80589e7	−	1.52522e8i	0.0119226	−	0.0206505i
$661$	3.29149e9	+	5.70103e9i	0.443290	+	0.767801i	0.997931	−	0.0642888i	$-0.0204779\pi$
$661$	3.29149e9	+	5.70103e9i	0.443290	+	0.767801i	−0.554641	+	0.832089i	$0.687145\pi$
$662$	1.09503e9	+	1.89664e9i	0.146697	+	0.254087i
$663$	−1.21942e8	+	2.11210e8i	−0.0162501	+	0.0281460i
$664$	−2.90452e9			−0.385023
$665$		0			0
$666$	2.62364e9			0.344147
$667$	3.52389e9	−	6.10357e9i	0.459814	−	0.796422i
$668$	2.80725e9	+	4.86230e9i	0.364387	+	0.631137i
$669$	8.78744e7	+	1.52203e8i	0.0113467	+	0.0196531i
$670$	1.05843e8	−	1.83326e8i	0.0135957	−	0.0235485i
$671$	9.03851e8			0.115496
$672$		0			0
$673$	−8.54649e9			−1.08077			−0.540387	−	0.841416i	$-0.681722\pi$
$673$	−8.54649e9			−1.08077			−0.540387	+	0.841416i	$0.681722\pi$
$674$	−3.67405e8	+	6.36364e8i	−0.0462206	+	0.0800564i
$675$	−8.63554e8	−	1.49572e9i	−0.108075	−	0.187192i
$676$	1.94683e9	+	3.37202e9i	0.242391	+	0.419833i
$677$	−4.35652e9	+	7.54572e9i	−0.539610	+	0.934631i	0.459315	+	0.888273i	$0.348095\pi$
$677$	−4.35652e9	+	7.54572e9i	−0.539610	+	0.934631i	−0.998925	+	0.0463581i	$0.985238\pi$
$678$	−1.59312e9			−0.196311
$679$		0			0
$680$	1.58119e9			0.192842
$681$	1.10725e9	−	1.91781e9i	0.134347	−	0.232696i
$682$	9.93947e8	+	1.72157e9i	0.119983	+	0.207816i
$683$	−7.30543e9	−	1.26534e10i	−0.877351	−	1.51962i	−0.854237	−	0.519884i	$-0.825975\pi$
$683$	−7.30543e9	−	1.26534e10i	−0.877351	−	1.51962i	−0.0231144	−	0.999733i	$-0.507358\pi$
$684$	−2.61112e9	+	4.52259e9i	−0.311982	+	0.540369i
$685$	6.62873e7			0.00787977
$686$		0			0
$687$	−1.05055e8			−0.0123615
$688$	1.29177e9	−	2.23741e9i	0.151226	−	0.261931i
$689$	1.03237e9	+	1.78811e9i	0.120245	+	0.208270i
$690$	−6.92617e8	−	1.19965e9i	−0.0802641	−	0.139021i
$691$	7.36738e9	−	1.27607e10i	0.849454	−	1.47130i	−0.0322413	−	0.999480i	$-0.510265\pi$
$691$	7.36738e9	−	1.27607e10i	0.849454	−	1.47130i	0.881696	−	0.471818i	$-0.156402\pi$
$692$	5.48451e8			0.0629167
$693$		0			0
$694$	1.09360e10			1.24194
$695$	4.11640e9	−	7.12981e9i	0.465126	−	0.805622i
$696$	−3.15095e8	−	5.45761e8i	−0.0354249	−	0.0613578i
$697$	−7.97212e7	−	1.38081e8i	−0.00891783	−	0.0154461i
$698$	4.52573e9	−	7.83879e9i	0.503726	−	0.872480i
$699$	−1.43467e9			−0.158885
$700$		0			0
$701$	1.31502e9			0.144185			0.0720923	−	0.997398i	$-0.477032\pi$
$701$	1.31502e9			0.144185			0.0720923	+	0.997398i	$0.477032\pi$
$702$	−2.80601e8	+	4.86016e8i	−0.0306133	+	0.0530237i
$703$	3.20570e9	+	5.55244e9i	0.348000	+	0.602754i
$704$	−1.43131e8	−	2.47910e8i	−0.0154607	−	0.0267787i
$705$	5.95547e8	−	1.03152e9i	0.0640109	−	0.110870i
$706$	3.58716e8			0.0383649
$707$		0			0
$708$	2.02803e9			0.214762
$709$	−3.32014e8	+	5.75065e8i	−0.0349860	+	0.0605976i	−0.882988	−	0.469395i	$-0.844472\pi$
$709$	−3.32014e8	+	5.75065e8i	−0.0349860	+	0.0605976i	0.848002	+	0.529993i	$0.177805\pi$
$710$	1.18837e9	+	2.05832e9i	0.124609	+	0.215828i
$711$	−3.64349e9	−	6.31070e9i	−0.380166	−	0.658467i
$712$	−3.05950e9	+	5.29922e9i	−0.317666	+	0.550214i
$713$	1.56356e10			1.61547
$714$		0			0
$715$	−3.16920e8			−0.0324249
$716$	−6.01730e8	+	1.04223e9i	−0.0612641	+	0.106113i
$717$	−2.37725e9	−	4.11753e9i	−0.240857	−	0.417176i
$718$	1.59312e9	+	2.75937e9i	0.160625	+	0.278211i
$719$	−2.47517e9	+	4.28712e9i	−0.248344	+	0.430145i	−0.963067	−	0.269263i	$-0.913220\pi$
$719$	−2.47517e9	+	4.28712e9i	−0.248344	+	0.430145i	0.714722	+	0.699408i	$0.246553\pi$
$720$	1.75731e9			0.175462
$721$		0			0
$722$	−5.61065e9			−0.554796
$723$	1.53964e9	−	2.66673e9i	0.151508	−	0.262419i
$724$	1.91880e9	+	3.32346e9i	0.187908	+	0.325466i
$725$	−1.74497e9	−	3.02238e9i	−0.170061	−	0.294555i
$726$	−8.78146e8	+	1.52099e9i	−0.0851704	+	0.147519i
$727$	8.81101e9			0.850463			0.425231	−	0.905085i	$-0.360193\pi$
$727$	8.81101e9			0.850463			0.425231	+	0.905085i	$0.360193\pi$
$728$		0			0
$729$	−6.55163e9			−0.626330
$730$	−8.23437e8	+	1.42623e9i	−0.0783430	+	0.135694i
$731$	4.63789e9	+	8.03306e9i	0.439147	+	0.760624i
$732$	−3.17838e8	−	5.50511e8i	−0.0299514	−	0.0518773i
$733$	7.47069e7	−	1.29396e8i	0.00700643	−	0.0121355i	−0.862501	−	0.506055i	$-0.831103\pi$
$733$	7.47069e7	−	1.29396e8i	0.00700643	−	0.0121355i	0.869507	+	0.493920i	$0.164436\pi$
$734$	−1.30777e10			−1.22066
$735$		0			0
$736$	−2.25155e9			−0.208166
$737$	6.87982e7	−	1.19162e8i	0.00633054	−	0.0109648i
$738$	−8.86008e7	−	1.53461e8i	−0.00811410	−	0.0140540i
$739$	2.35403e9	+	4.07730e9i	0.214564	+	0.371635i	0.953138	−	0.302537i	$-0.0978337\pi$
$739$	2.35403e9	+	4.07730e9i	0.214564	+	0.371635i	−0.738574	+	0.674173i	$0.764500\pi$
$740$	1.07873e9	−	1.86842e9i	0.0978596	−	0.169498i
$741$	−6.62365e8			−0.0598045
$742$		0			0
$743$	1.69676e9			0.151761			0.0758805	−	0.997117i	$-0.475823\pi$
$743$	1.69676e9			0.151761			0.0758805	+	0.997117i	$0.475823\pi$
$744$	6.99040e8	−	1.21077e9i	0.0622295	−	0.107785i
$745$	−2.29804e9	−	3.98031e9i	−0.203615	−	0.352671i
$746$	−6.18533e9	−	1.07133e10i	−0.545477	−	0.944794i
$747$	5.79486e9	−	1.00370e10i	0.508652	−	0.881011i
$748$	1.02777e9			0.0897928
$749$		0			0
$750$	−2.26094e9			−0.195693
$751$	−5.33250e9	+	9.23616e9i	−0.459400	+	0.795704i	−0.998929	−	0.0462626i	$-0.985269\pi$
$751$	−5.33250e9	+	9.23616e9i	−0.459400	+	0.795704i	0.539529	+	0.841967i	$0.318602\pi$
$752$	−9.67999e8	−	1.67662e9i	−0.0830066	−	0.143772i
$753$	4.40865e8	+	7.63601e8i	0.0376291	+	0.0651755i
$754$	−5.67007e8	+	9.82085e8i	−0.0481713	+	0.0834352i
$755$	6.17724e9			0.522373
$756$		0			0
$757$	6.22876e9			0.521874			0.260937	−	0.965356i	$-0.415968\pi$
$757$	6.22876e9			0.521874			0.260937	+	0.965356i	$0.415968\pi$
$758$	−4.22753e9	+	7.32229e9i	−0.352569	+	0.610668i
$759$	−4.50201e8	−	7.79771e8i	−0.0373732	−	0.0647323i
$760$	2.14717e9	+	3.71902e9i	0.177427	+	0.307313i
$761$	4.19167e9	−	7.26019e9i	0.344779	−	0.597175i	−0.640535	−	0.767929i	$-0.721287\pi$
$761$	4.19167e9	−	7.26019e9i	0.344779	−	0.597175i	0.985314	+	0.170755i	$0.0546205\pi$
$762$	−1.12153e8			−0.00918263
$763$		0			0
$764$	6.01511e9			0.487997
$765$	−3.15466e9	+	5.46403e9i	−0.254763	+	0.441263i
$766$	8.99640e8	+	1.55822e9i	0.0723216	+	0.125265i
$767$	−1.82470e9	−	3.16047e9i	−0.146018	−	0.252911i
$768$	−1.00663e8	+	1.74354e8i	−0.00801875	+	0.0138889i
$769$	−1.18649e10			−0.940852			−0.470426	−	0.882439i	$-0.655900\pi$
$769$	−1.18649e10			−0.940852			−0.470426	+	0.882439i	$0.655900\pi$
$770$		0			0
$771$	−2.43241e9			−0.191138
$772$	1.12623e9	−	1.95068e9i	0.0880978	−	0.152590i
$773$	−2.78340e9	−	4.82099e9i	−0.216744	−	0.375412i	0.737067	−	0.675820i	$-0.236210\pi$
$773$	−2.78340e9	−	4.82099e9i	−0.216744	−	0.375412i	−0.953811	+	0.300408i	$0.902877\pi$
$774$	5.15447e9	+	8.92781e9i	0.399568	+	0.692072i
$775$	3.87123e9	−	6.70516e9i	0.298740	−	0.517432i
$776$	−4.44526e9			−0.341492
$777$		0			0
$778$	−8.14306e9			−0.619953
$779$	2.16515e8	−	3.75015e8i	0.0164099	−	0.0284228i
$780$	1.11444e8	+	1.93028e8i	0.00840867	+	0.0145642i
$781$	7.72441e8	+	1.33791e9i	0.0580212	+	0.100496i
$782$	4.04191e9	−	7.00080e9i	0.302248	−	0.523509i
$783$	5.20645e9			0.387593
$784$		0			0
$785$	−1.27165e10			−0.938264
$786$	−3.80344e8	+	6.58775e8i	−0.0279381	+	0.0483903i
$787$	−6.73056e7	−	1.16577e8i	−0.00492198	−	0.00852512i	0.863554	−	0.504257i	$-0.168233\pi$
$787$	−6.73056e7	−	1.16577e8i	−0.00492198	−	0.00852512i	−0.868476	+	0.495731i	$0.834900\pi$
$788$	−3.29553e9	−	5.70803e9i	−0.239929	−	0.415570i
$789$	−9.25524e8	+	1.60306e9i	−0.0670839	+	0.116193i
$790$	−5.99222e9			−0.432408
$791$		0			0
$792$	1.14225e9			0.0817001
$793$	−5.71942e8	+	9.90633e8i	−0.0407283	+	0.0705434i
$794$	−5.90261e9	−	1.02236e10i	−0.418478	−	0.724825i
$795$	−1.88246e9	−	3.26052e9i	−0.132874	−	0.230145i
$796$	−2.67640e9	+	4.63566e9i	−0.188086	+	0.325774i
$797$	−7.41548e9			−0.518842			−0.259421	−	0.965764i	$-0.583532\pi$
$797$	−7.41548e9			−0.518842			−0.259421	+	0.965764i	$0.583532\pi$
$798$		0			0
$799$	6.95088e9			0.482088
$800$	−5.57466e8	+	9.65559e8i	−0.0384949	+	0.0666751i
$801$	−1.22081e10	−	2.11451e10i	−0.839336	−	1.45377i
$802$	1.09965e9	+	1.90465e9i	0.0752738	+	0.130378i
$803$	−5.35234e8	+	9.27052e8i	−0.0364787	+	0.0631829i
$804$	−9.67711e7			−0.00656673
$805$		0			0
$806$	−2.51581e9			−0.169241
$807$	3.74411e9	−	6.48499e9i	0.250779	−	0.434362i
$808$	−2.58036e9	−	4.46932e9i	−0.172084	−	0.298058i
$809$	7.07709e9	+	1.22579e10i	0.469932	+	0.813946i	0.999409	−	0.0343786i	$-0.0109452\pi$
$809$	7.07709e9	+	1.22579e10i	0.469932	+	0.813946i	−0.529477	+	0.848324i	$0.677612\pi$
$810$	−3.24149e9	+	5.61443e9i	−0.214313	+	0.371200i
$811$	−2.63708e10			−1.73600			−0.868001	−	0.496563i	$-0.834595\pi$
$811$	−2.63708e10			−1.73600			−0.868001	+	0.496563i	$0.834595\pi$
$812$		0			0
$813$	−4.65580e9			−0.303863
$814$	7.01178e8	−	1.21448e9i	0.0455662	−	0.0789229i
$815$	5.99396e9	+	1.03818e10i	0.387848	+	0.671773i
$816$	−3.61415e8	−	6.25989e8i	−0.0232857	−	0.0403321i
$817$	−1.25960e10	+	2.18170e10i	−0.808084	+	1.39964i
$818$	1.30742e10			0.835176
$819$		0			0
$820$	−1.45716e8			−0.00922912
$821$	−4.03132e9	+	6.98245e9i	−0.254241	+	0.440359i	−0.964689	−	0.263391i	$-0.915159\pi$
$821$	−4.03132e9	+	6.98245e9i	−0.254241	+	0.440359i	0.710448	+	0.703750i	$0.248492\pi$
$822$	−1.51514e7	−	2.62430e7i	−0.000951483	−	0.00164802i
$823$	1.17101e10	+	2.02825e10i	0.732253	+	1.26830i	0.955918	+	0.293633i	$0.0948643\pi$
$823$	1.17101e10	+	2.02825e10i	0.732253	+	1.26830i	−0.223666	+	0.974666i	$0.571802\pi$
$824$	9.59486e8	−	1.66188e9i	0.0597439	−	0.103479i
$825$	−4.45864e8			−0.0276448
$826$		0			0
$827$	5.55722e9			0.341655			0.170828	−	0.985301i	$-0.445356\pi$
$827$	5.55722e9			0.341655			0.170828	+	0.985301i	$0.445356\pi$
$828$	4.49212e9	−	7.78057e9i	0.275008	−	0.476327i
$829$	−1.42128e10	−	2.46173e10i	−0.866440	−	1.50072i	−0.865610	−	0.500718i	$-0.833069\pi$
$829$	−1.42128e10	−	2.46173e10i	−0.866440	−	1.50072i	−0.000829498	−	1.00000i	$-0.500264\pi$
$830$	−4.76523e9	−	8.25362e9i	−0.289275	−	0.501039i
$831$	−2.72371e9	+	4.71761e9i	−0.164649	+	0.285180i
$832$	3.62283e8			0.0218080
$833$		0			0
$834$	−3.76356e9			−0.224656
$835$	−9.21128e9	+	1.59544e10i	−0.547542	+	0.948371i
$836$	1.39566e9	+	2.41736e9i	0.0826150	+	0.143093i
$837$	5.77527e9	+	1.00031e10i	0.340434	+	0.589649i
$838$	−4.45119e9	+	7.70969e9i	−0.261290	+	0.452567i
$839$	1.04036e10			0.608156			0.304078	−	0.952647i	$-0.401652\pi$
$839$	1.04036e10			0.608156			0.304078	+	0.952647i	$0.401652\pi$
$840$		0			0
$841$	−6.72927e9			−0.390105
$842$	3.69011e9	−	6.39146e9i	0.213033	−	0.368984i
$843$	−2.00262e9	−	3.46864e9i	−0.115134	−	0.199417i
$844$	3.11683e9	+	5.39851e9i	0.178449	+	0.309083i
$845$	−6.38805e9	+	1.10644e10i	−0.364225	+	0.630857i
$846$	7.72509e9			0.438639
$847$		0			0
$848$	−6.11950e9			−0.344612
$849$	−3.22617e9	+	5.58789e9i	−0.180930	+	0.313380i
$850$	−2.00149e9	−	3.46668e9i	−0.111786	−	0.193619i
$851$	−5.51503e9	−	9.55231e9i	−0.306757	−	0.531319i
$852$	5.43256e8	−	9.40946e8i	0.0300930	−	0.0521226i
$853$	−1.80580e10			−0.996205			−0.498102	−	0.867118i	$-0.665970\pi$
$853$	−1.80580e10			−0.996205			−0.498102	+	0.867118i	$0.665970\pi$
$854$		0			0
$855$	−1.71355e10			−0.937593
$856$	−4.60430e9	+	7.97489e9i	−0.250903	+	0.434577i
$857$	3.17017e9	+	5.49090e9i	0.172048	+	0.297996i	0.939136	−	0.343546i	$-0.111628\pi$
$857$	3.17017e9	+	5.49090e9i	0.172048	+	0.297996i	−0.767088	+	0.641542i	$0.778295\pi$
$858$	7.24389e7	+	1.25468e8i	0.00391531	+	0.00678152i
$859$	−6.07444e9	+	1.05212e10i	−0.326987	+	0.566358i	−0.981912	−	0.189336i	$-0.939367\pi$
$859$	−6.07444e9	+	1.05212e10i	−0.326987	+	0.566358i	0.654926	+	0.755693i	$0.272700\pi$
$860$	8.47725e9			0.454476
$861$		0			0
$862$	7.85206e9			0.417550
$863$	1.43556e10	−	2.48646e10i	0.760295	−	1.31687i	−0.182403	−	0.983224i	$-0.558388\pi$
$863$	1.43556e10	−	2.48646e10i	0.760295	−	1.31687i	0.942698	−	0.333646i	$-0.108279\pi$
$864$	−8.31652e8	−	1.44046e9i	−0.0438676	−	0.0759808i
$865$	8.99802e8	+	1.55850e9i	0.0472705	+	0.0818750i
$866$	1.13999e10	−	1.97452e10i	0.596471	−	1.03312i
$867$	−2.32887e9			−0.121361
$868$		0			0
$869$	−3.89495e9			−0.201341
$870$	1.03391e9	−	1.79078e9i	0.0532309	−	0.0921986i
$871$	8.70688e7	+	1.50808e8i	0.00446477	+	0.00773320i
$872$	3.13780e9	+	5.43483e9i	0.160257	+	0.277574i
$873$	8.86881e9	−	1.53612e10i	0.451144	−	0.781405i
$874$	2.19549e10			1.11235
$875$		0			0
$876$	7.52857e8			0.0378397
$877$	−1.23011e10	+	2.13061e10i	−0.615806	+	1.06661i	0.374437	+	0.927253i	$0.377836\pi$
$877$	−1.23011e10	+	2.13061e10i	−0.615806	+	1.06661i	−0.990243	+	0.139355i	$0.955497\pi$
$878$	−4.22487e9	−	7.31770e9i	−0.210660	−	0.364875i
$879$	−2.01360e9	−	3.48766e9i	−0.100003	−	0.173210i
$880$	4.69647e8	−	8.13453e8i	0.0232318	−	0.0402386i
$881$	−1.25378e10			−0.617738			−0.308869	−	0.951105i	$-0.599951\pi$
$881$	−1.25378e10			−0.617738			−0.308869	+	0.951105i	$0.599951\pi$
$882$		0			0
$883$	1.93097e10			0.943873			0.471937	−	0.881633i	$-0.343555\pi$
$883$	1.93097e10			0.943873			0.471937	+	0.881633i	$0.343555\pi$
$884$	−6.50358e8	+	1.12645e9i	−0.0316643	+	0.0548441i
$885$	3.32723e9	+	5.76293e9i	0.161355	+	0.279475i
$886$	7.29302e9	+	1.26319e10i	0.352281	+	0.610169i
$887$	−1.60134e10	+	2.77360e10i	−0.770462	+	1.33448i	0.166848	+	0.985983i	$0.446641\pi$
$887$	−1.60134e10	+	2.77360e10i	−0.770462	+	1.33448i	−0.937310	+	0.348496i	$0.886692\pi$
$888$	−9.86272e8			−0.0472663
$889$		0			0
$890$	−2.00780e10			−0.954675
$891$	−2.10697e9	+	3.64938e9i	−0.0997899	+	0.172841i
$892$	4.68663e8	+	8.11749e8i	0.0221098	+	0.0382952i
$893$	9.43894e9	+	1.63487e10i	0.443551	+	0.768252i
$894$	−1.05053e9	+	1.81957e9i	−0.0491731	+	0.0851703i
$895$	−3.94885e9			−0.184115
$896$		0			0
$897$	1.13952e9			0.0527167
$898$	7.39384e9	−	1.28065e10i	0.340724	−	0.590151i
$899$	1.16700e10	+	2.02130e10i	0.535688	+	0.927839i
$900$	−2.22442e9	−	3.85281e9i	−0.101711	−	0.176169i
$901$	1.09855e10	−	1.90275e10i	0.500361	−	0.866651i
$902$	−9.47157e7			−0.00429733
$903$		0			0
$904$	−8.49662e9			−0.382522
$905$	−6.29606e9	+	1.09051e10i	−0.282357	+	0.489057i
$906$	−1.41194e9	−	2.44555e9i	−0.0630766	−	0.109252i
$907$	−1.16852e9	−	2.02393e9i	−0.0520008	−	0.0900679i	0.838853	−	0.544357i	$-0.183226\pi$
$907$	−1.16852e9	−	2.02393e9i	−0.0520008	−	0.0900679i	−0.890854	+	0.454290i	$0.849893\pi$
$908$	5.90531e9	−	1.02283e10i	0.261783	−	0.453422i
$909$	2.05925e10			0.909359
$910$		0			0
$911$	2.20343e10			0.965573			0.482786	−	0.875738i	$-0.339625\pi$
$911$	2.20343e10			0.965573			0.482786	+	0.875738i	$0.339625\pi$
$912$	9.81565e8	−	1.70012e9i	0.0428487	−	0.0742161i
$913$	−3.09740e9	−	5.36485e9i	−0.134694	−	0.233297i
$914$	−1.19226e10	−	2.06506e10i	−0.516489	−	0.894585i
$915$	1.04290e9	−	1.80636e9i	0.0450060	−	0.0779527i
$916$	−5.60295e8			−0.0240870
$917$		0			0
$918$	5.97181e9			0.254775
$919$	7.16387e9	−	1.24082e10i	0.304469	−	0.527356i	−0.672674	−	0.739939i	$-0.734854\pi$
$919$	7.16387e9	−	1.24082e10i	0.304469	−	0.527356i	0.977143	+	0.212583i	$0.0681876\pi$
$920$	−3.69396e9	−	6.39812e9i	−0.156399	−	0.270891i
$921$	−1.29017e9	−	2.23465e9i	−0.0544176	−	0.0942541i
$922$	−1.01112e10	+	1.75132e10i	−0.424860	+	0.735879i
$923$	−1.95515e9			−0.0818418
$924$		0			0
$925$	−5.46190e9			−0.226907
$926$	−3.56116e9	+	6.16812e9i	−0.147385	+	0.255278i
$927$	3.82857e9	+	6.63128e9i	0.157855	+	0.273413i
$928$	−1.68051e9	−	2.91072e9i	−0.0690275	−	0.119559i
$929$	−6.56399e9	+	1.13692e10i	−0.268604	+	0.465236i	−0.968502	−	0.249007i	$-0.919896\pi$
$929$	−6.56399e9	+	1.13692e10i	−0.268604	+	0.465236i	0.699898	+	0.714243i	$0.253229\pi$
$930$	4.58745e9			0.187017
$931$		0			0
$932$	−7.65160e9			−0.309597
$933$	−4.75237e9	+	8.23134e9i	−0.191569	+	0.331807i
$934$	1.06267e10	+	1.84059e10i	0.426759	+	0.739169i
$935$	1.68619e9	+	2.92057e9i	0.0674630	+	0.116849i
$936$	−7.22797e8	+	1.25192e9i	−0.0288105	+	0.0499013i
$937$	−3.87626e10			−1.53930			−0.769652	−	0.638463i	$-0.779571\pi$
$937$	−3.87626e10			−1.53930			−0.769652	+	0.638463i	$0.779571\pi$
$938$		0			0
$939$	−1.42149e9			−0.0560291
$940$	3.17625e9	−	5.50142e9i	0.124729	−	0.216037i
$941$	−1.03140e10	−	1.78643e10i	−0.403517	−	0.698912i	0.590630	−	0.806942i	$-0.298879\pi$
$941$	−1.03140e10	−	1.78643e10i	−0.403517	−	0.698912i	−0.994148	+	0.108030i	$0.965546\pi$
$942$	2.90664e9	+	5.03445e9i	0.113296	+	0.196234i
$943$	−3.72488e8	+	6.45168e8i	−0.0144651	+	0.0250543i
$944$	1.08161e10			0.418476
$945$		0			0
$946$	5.51021e9			0.211617
$947$	1.05853e10	−	1.83342e10i	0.405020	−	0.701516i	−0.589304	−	0.807912i	$-0.700598\pi$
$947$	1.05853e10	−	1.83342e10i	0.405020	−	0.701516i	0.994324	+	0.106396i	$0.0339311\pi$
$948$	1.36965e9	+	2.37231e9i	0.0522133	+	0.0904360i
$949$	−6.77375e8	−	1.17325e9i	−0.0257275	−	0.0445613i
$950$	5.43583e9	−	9.41514e9i	0.205700	−	0.356282i
$951$	−6.08771e8			−0.0229521
$952$		0			0
$953$	2.14876e10			0.804196			0.402098	−	0.915597i	$-0.368281\pi$
$953$	2.14876e10			0.804196			0.402098	+	0.915597i	$0.368281\pi$
$954$	1.22091e10	−	2.11468e10i	0.455266	−	0.788543i
$955$	9.86854e9	+	1.70928e10i	0.366641	+	0.635041i
$956$	−1.26787e10	−	2.19601e10i	−0.469323	−	0.812891i
$957$	6.72039e8	−	1.16401e9i	0.0247858	−	0.0429302i
$958$	−1.04075e10			−0.382442
$959$		0			0
$960$	−6.60603e8			−0.0240986
$961$	−1.21336e10	+	2.10161e10i	−0.441021	+	0.763871i
$962$	8.87388e8	+	1.53700e9i	0.0321367	+	0.0556623i
$963$	−1.83723e10	−	3.18217e10i	−0.662934	−	1.14824i
$964$	8.21140e9	−	1.42226e10i	0.295221	−	0.511338i
$965$	7.39086e9			0.264758
$966$		0			0
$967$	3.92625e10			1.39632			0.698161	−	0.715941i	$-0.254002\pi$
$967$	3.92625e10			1.39632			0.698161	+	0.715941i	$0.254002\pi$
$968$	−4.68344e9	+	8.11196e9i	−0.165959	+	0.287450i
$969$	3.52415e9	+	6.10400e9i	0.124429	+	0.215517i
$970$	−7.29300e9	−	1.26319e10i	−0.256570	−	0.444392i
$971$	2.81323e10	−	4.87266e10i	0.986140	−	1.70804i	0.349381	−	0.936981i	$-0.386392\pi$
$971$	2.81323e10	−	4.87266e10i	0.986140	−	1.70804i	0.636759	−	0.771063i	$-0.280275\pi$
$972$	1.00684e10			0.351665
$973$		0			0
$974$	8.59573e9			0.298076
$975$	2.82135e8	−	4.88673e8i	0.00974858	−	0.0168850i
$976$	−1.69513e9	−	2.93606e9i	−0.0583619	−	0.101086i
$977$	4.21718e9	+	7.30438e9i	0.144674	+	0.250583i	0.929251	−	0.369448i	$-0.120453\pi$
$977$	4.21718e9	+	7.30438e9i	0.144674	+	0.250583i	−0.784577	+	0.620031i	$0.787120\pi$
$978$	2.74009e9	−	4.74598e9i	0.0936655	−	0.162233i
$979$	−1.30507e10			−0.444523
$980$		0			0
$981$	−2.50411e10			−0.846861
$982$	−3.13338e9	+	5.42717e9i	−0.105590	+	0.182887i
$983$	1.12115e10	+	1.94189e10i	0.376466	+	0.652058i	0.990545	−	0.137186i	$-0.0438059\pi$
$983$	1.12115e10	+	1.94189e10i	0.376466	+	0.652058i	−0.614079	+	0.789244i	$0.710473\pi$
$984$	3.33066e7	+	5.76888e7i	0.00111442	+	0.00193023i
$985$	1.08135e10	−	1.87295e10i	0.360527	−	0.624451i
$986$	1.20672e10			0.400900
$987$		0			0
$988$	−3.53261e9			−0.116532
$989$	2.16700e10	−	3.75335e10i	0.712314	−	1.23376i
$990$	1.87400e9	+	3.24587e9i	0.0613829	+	0.106318i
$991$	−1.73364e10	−	3.00275e10i	−0.565849	−	0.980079i	−0.996970	−	0.0777853i	$-0.975215\pi$
$991$	−1.73364e10	−	3.00275e10i	−0.565849	−	0.980079i	0.431121	−	0.902294i	$-0.358118\pi$
$992$	3.72821e9	−	6.45745e9i	0.121258	−	0.210025i
$993$	3.28508e9			0.106469
$994$		0			0
$995$	−1.75639e10			−0.565249
$996$	−2.17839e9	+	3.77308e9i	−0.0698599	+	0.121001i
$997$	1.48237e10	+	2.56754e10i	0.473722	+	0.820511i	0.999547	−	0.0300818i	$-0.00957679\pi$
$997$	1.48237e10	+	2.56754e10i	0.473722	+	0.820511i	−0.525825	+	0.850593i	$0.676243\pi$
$998$	−2.49275e9	−	4.31757e9i	−0.0793820	−	0.137494i
$999$	4.07415e9	−	7.05663e9i	0.129288	−	0.223933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.8.c.d.79.1		2
7.2	even	3		2.8.a.a.1.1	✓	1
7.3	odd	6		98.8.c.e.67.1		2
7.4	even	3	inner	98.8.c.d.67.1		2
7.5	odd	6		98.8.a.a.1.1		1
7.6	odd	2		98.8.c.e.79.1		2
21.2	odd	6		18.8.a.b.1.1		1
28.23	odd	6		16.8.a.b.1.1		1
35.2	odd	12		50.8.b.c.49.1		2
35.9	even	6		50.8.a.g.1.1		1
35.23	odd	12		50.8.b.c.49.2		2
56.37	even	6		64.8.a.c.1.1		1
56.51	odd	6		64.8.a.e.1.1		1
63.2	odd	6		162.8.c.a.109.1		2
63.16	even	3		162.8.c.l.109.1		2
63.23	odd	6		162.8.c.a.55.1		2
63.58	even	3		162.8.c.l.55.1		2
77.65	odd	6		242.8.a.e.1.1		1
84.23	even	6		144.8.a.i.1.1		1
91.44	odd	12		338.8.b.d.337.2		2
91.51	even	6		338.8.a.d.1.1		1
91.86	odd	12		338.8.b.d.337.1		2
105.2	even	12		450.8.c.g.199.2		2
105.23	even	12		450.8.c.g.199.1		2
105.44	odd	6		450.8.a.c.1.1		1
112.37	even	12		256.8.b.b.129.1		2
112.51	odd	12		256.8.b.f.129.1		2
112.93	even	12		256.8.b.b.129.2		2
112.107	odd	12		256.8.b.f.129.2		2
119.16	even	6		578.8.a.b.1.1		1
140.23	even	12		400.8.c.j.49.1		2
140.79	odd	6		400.8.a.l.1.1		1
140.107	even	12		400.8.c.j.49.2		2
168.107	even	6		576.8.a.f.1.1		1
168.149	odd	6		576.8.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.8.a.a.1.1	✓	1	7.2	even	3
16.8.a.b.1.1		1	28.23	odd	6
18.8.a.b.1.1		1	21.2	odd	6
50.8.a.g.1.1		1	35.9	even	6
50.8.b.c.49.1		2	35.2	odd	12
50.8.b.c.49.2		2	35.23	odd	12
64.8.a.c.1.1		1	56.37	even	6
64.8.a.e.1.1		1	56.51	odd	6
98.8.a.a.1.1		1	7.5	odd	6
98.8.c.d.67.1		2	7.4	even	3	inner
98.8.c.d.79.1		2	1.1	even	1	trivial
98.8.c.e.67.1		2	7.3	odd	6
98.8.c.e.79.1		2	7.6	odd	2
144.8.a.i.1.1		1	84.23	even	6
162.8.c.a.55.1		2	63.23	odd	6
162.8.c.a.109.1		2	63.2	odd	6
162.8.c.l.55.1		2	63.58	even	3
162.8.c.l.109.1		2	63.16	even	3
242.8.a.e.1.1		1	77.65	odd	6
256.8.b.b.129.1		2	112.37	even	12
256.8.b.b.129.2		2	112.93	even	12
256.8.b.f.129.1		2	112.51	odd	12
256.8.b.f.129.2		2	112.107	odd	12
338.8.a.d.1.1		1	91.51	even	6
338.8.b.d.337.1		2	91.86	odd	12
338.8.b.d.337.2		2	91.44	odd	12
400.8.a.l.1.1		1	140.79	odd	6
400.8.c.j.49.1		2	140.23	even	12
400.8.c.j.49.2		2	140.107	even	12
450.8.a.c.1.1		1	105.44	odd	6
450.8.c.g.199.1		2	105.23	even	12
450.8.c.g.199.2		2	105.2	even	12
576.8.a.f.1.1		1	168.107	even	6
576.8.a.g.1.1		1	168.149	odd	6
578.8.a.b.1.1		1	119.16	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-6.00000 - 10.3923i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(105.000 - 181.865i) q^{5} -96.0000 q^{6} -512.000 q^{8} +(1021.50 - 1769.29i) q^{9} +(-840.000 - 1454.92i) q^{10} +(-546.000 - 945.700i) q^{11} +(-384.000 + 665.108i) q^{12} +1382.00 q^{13} -2520.00 q^{15} +(-2048.00 + 3547.24i) q^{16} +(-7353.00 - 12735.8i) q^{17} +(-8172.00 - 14154.3i) q^{18} +(19970.0 - 34589.1i) q^{19} -13440.0 q^{20} -8736.00 q^{22} +(-34356.0 + 59506.3i) q^{23} +(3072.00 + 5320.86i) q^{24} +(17012.5 + 29466.5i) q^{25} +(5528.00 - 9574.78i) q^{26} -50760.0 q^{27} -102570. q^{29} +(-10080.0 + 17459.1i) q^{30} +(-113776. - 197066. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-6552.00 + 11348.4i) q^{33} -117648. q^{34} -130752. q^{36} +(-80263.0 + 139020. i) q^{37} +(-159760. - 276712. i) q^{38} +(-8292.00 - 14362.2i) q^{39} +(-53760.0 + 93115.1i) q^{40} +10842.0 q^{41} -630748. q^{43} +(-34944.0 + 60524.8i) q^{44} +(-214515. - 371551. i) q^{45} +(274848. + 476051. i) q^{46} +(-236328. + 409332. i) q^{47} +49152.0 q^{48} +272200. q^{50} +(-88236.0 + 152829. i) q^{51} +(-44224.0 - 76598.2i) q^{52} +(747009. + 1.29386e6i) q^{53} +(-203040. + 351676. i) q^{54} -229320. q^{55} -479280. q^{57} +(-410280. + 710626. i) q^{58} +(-1.32033e6 - 2.28688e6i) q^{59} +(80640.0 + 139673. i) q^{60} +(-413851. + 716811. i) q^{61} -1.82042e6 q^{62} +262144. q^{64} +(145110. - 251338. i) q^{65} +(52416.0 + 90787.2i) q^{66} +(63002.0 + 109123. i) q^{67} +(-470592. + 815089. i) q^{68} +824544. q^{69} -1.41473e6 q^{71} +(-523008. + 905876. i) q^{72} +(-490141. - 848949. i) q^{73} +(642104. + 1.11216e6i) q^{74} +(204150. - 353598. i) q^{75} -2.55616e6 q^{76} -132672. q^{78} +(1.78340e6 - 3.08894e6i) q^{79} +(430080. + 744920. i) q^{80} +(-1.92946e6 - 3.34192e6i) q^{81} +(43368.0 - 75115.6i) q^{82} +5.67289e6 q^{83} -3.08826e6 q^{85} +(-2.52299e6 + 4.36995e6i) q^{86} +(615420. + 1.06594e6i) q^{87} +(279552. + 484198. i) q^{88} +(5.97560e6 - 1.03500e7i) q^{89} -3.43224e6 q^{90} +4.39757e6 q^{92} +(-1.36531e6 + 2.36479e6i) q^{93} +(1.89062e6 + 3.27466e6i) q^{94} +(-4.19370e6 - 7.26370e6i) q^{95} +(196608. - 340535. i) q^{96} +8.68215e6 q^{97} -2.23096e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 12 q^{3} - 64 q^{4} + 210 q^{5} - 192 q^{6} - 1024 q^{8} + 2043 q^{9} - 1680 q^{10} - 1092 q^{11} - 768 q^{12} + 2764 q^{13} - 5040 q^{15} - 4096 q^{16} - 14706 q^{17} - 16344 q^{18} + 39940 q^{19}+ \cdots - 4461912 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 12 * q^3 - 64 * q^4 + 210 * q^5 - 192 * q^6 - 1024 * q^8 + 2043 * q^9 - 1680 * q^10 - 1092 * q^11 - 768 * q^12 + 2764 * q^13 - 5040 * q^15 - 4096 * q^16 - 14706 * q^17 - 16344 * q^18 + 39940 * q^19 - 26880 * q^20 - 17472 * q^22 - 68712 * q^23 + 6144 * q^24 + 34025 * q^25 + 11056 * q^26 - 101520 * q^27 - 205140 * q^29 - 20160 * q^30 - 227552 * q^31 + 32768 * q^32 - 13104 * q^33 - 235296 * q^34 - 261504 * q^36 - 160526 * q^37 - 319520 * q^38 - 16584 * q^39 - 107520 * q^40 + 21684 * q^41 - 1261496 * q^43 - 69888 * q^44 - 429030 * q^45 + 549696 * q^46 - 472656 * q^47 + 98304 * q^48 + 544400 * q^50 - 176472 * q^51 - 88448 * q^52 + 1494018 * q^53 - 406080 * q^54 - 458640 * q^55 - 958560 * q^57 - 820560 * q^58 - 2640660 * q^59 + 161280 * q^60 - 827702 * q^61 - 3640832 * q^62 + 524288 * q^64 + 290220 * q^65 + 104832 * q^66 + 126004 * q^67 - 941184 * q^68 + 1649088 * q^69 - 2829456 * q^71 - 1046016 * q^72 - 980282 * q^73 + 1284208 * q^74 + 408300 * q^75 - 5112320 * q^76 - 265344 * q^78 + 3566800 * q^79 + 860160 * q^80 - 3858921 * q^81 + 86736 * q^82 + 11345784 * q^83 - 6176520 * q^85 - 5045984 * q^86 + 1230840 * q^87 + 559104 * q^88 + 11951190 * q^89 - 6864480 * q^90 + 8795136 * q^92 - 2730624 * q^93 + 3781248 * q^94 - 8387400 * q^95 + 393216 * q^96 + 17364292 * q^97 - 4461912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more